Two-dimensional standard normal distribution probability numerical calculation method, device, equipment, medium and product

Abstract

The invention discloses a two-dimensional standard normal distribution probability numerical calculation method and device, equipment, a medium and a product, and relates to the field of two-dimensional standard normal distribution probability numerical calculation, and the method comprises the steps: selecting an x axial step length hx and a y axial step length hy according to the precision requirement, dividing the forward boundary curve into a plurality of directed arc segments according to the key node of the forward boundary curve of the integral region and the y axial step length hy; carrying out integration on the abscissa variable, and constructing a function by utilizing a Taylor formula and a partial integration method; on the basis of the constructed function, converting a two-dimensional standard normal distribution probability calculation problem into a curve integral problem of a vertical coordinate variable, and calculating an approximate value of the curve integral of the vertical coordinate variable on each directed arc section; and determining a two-dimensional standard normal distribution probability according to the approximate values of the curve integrals of the ordinate variables on all the directed arc segments. The method can improve the calculation efficiency.

Description

Technical Field

[0001] The present application relates to the field of numerical calculation of two-dimensional standard normal distribution probability, and in particular to a method, device, equipment, medium and product for numerical calculation of two-dimensional standard normal distribution probability. Background Art

[0002] In the problems of error data analysis, structural system reliability analysis, resource delivery, component parameter selection, etc., it is usually necessary to calculate a large number of two-dimensional standard normal distribution probabilities on irregular integral regions in order to select appropriate parameters to maximize a certain benefit (corresponding to the maximum probability). This problem is a special two-dimensional standard normal distribution probability calculation problem.

[0003] Assuming that the irregular integral region is a complex polygonal region or a curved polygonal region, the normal distribution probability required can be regarded as a double integral on the irregular integral region. In order to obtain a probability that meets the accuracy requirements, the existing double integral numerical calculation method needs to be used to grid the integral region into multiple sub-regions and calculate the probability on the corresponding sub-regions. However, due to the low integral accuracy caused by the shape of the integral region and the large amount of numerical calculation, the calculation efficiency is low. Especially in emergency situations such as sudden situations and emergency rescue, the calculation time required for the calculation of the probability of two-dimensional standard normal distribution on multiple different complex integral regions using the existing method is long and cannot meet the needs of actual work. There is an urgent need for methods to further improve the efficiency of numerical calculation of the probability of two-dimensional standard normal distribution. Summary of the invention

[0004] The purpose of this application is to provide a two-dimensional standard normal distribution probability numerical calculation method, device, equipment, medium and product to solve the problem of low calculation efficiency of the existing double integral numerical calculation method.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a two-dimensional standard normal distribution probability numerical calculation method, comprising:

[0007] Select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value;

[0008] Integrate the abscissa variable and construct the function using Taylor's formula and integration by parts;

[0009] Based on the constructed function, the probability calculation problem of the two-dimensional standard normal distribution is converted into a curve integral problem of the ordinate variable, and the approximate value of the curve integral of the ordinate variable is calculated on each directed arc segment;

[0010] Determine the two-dimensional standard normal distribution probability based on the approximation of the curve integral of the ordinate variable over all directed arc segments.

[0011] In a second aspect, the present application provides a two-dimensional standard normal distribution probability numerical calculation device, comprising:

[0012] Segmentation module, used to select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value;

[0013] Function construction module, used to integrate the horizontal axis variable and construct functions using Taylor's formula and integration by parts method;

[0014] The approximate value calculation module of the curve integral is used to convert the probability calculation problem of the two-dimensional standard normal distribution into the curve integral problem of the ordinate variable based on the constructed function, and calculate the approximate value of the curve integral of the ordinate variable on each directed arc segment;

[0015] The two-dimensional standard normal distribution probability determination module is used to determine the two-dimensional standard normal distribution probability according to the approximate value of the curve integral of the ordinate variable on all directed arc segments.

[0016] In a third aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any one of the above-mentioned two-dimensional standard normal distribution probability numerical calculation methods.

[0017] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned two-dimensional standard normal distribution probability numerical calculation methods.

[0018] In a fifth aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements any of the above-mentioned two-dimensional standard normal distribution probability numerical calculation methods.

[0019] According to the specific embodiments provided by the present application, the present application discloses the following technical effects: the present application converts the two-dimensional standard normal distribution probability calculation problem into a curve integration problem for coordinates by dividing the forward boundary curve into multiple directed arc segments and constructing a function, and calculates the curve integral of the vertical coordinate variable on each directed arc segment, thereby obtaining the two-dimensional standard normal distribution probability, overcoming the problems of low integration accuracy and excessive numerical calculation caused by the shape of the integration area, and improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 This is a flow chart of a two-dimensional standard normal distribution probability numerical calculation method in one embodiment of the present application;

[0022] Figure 2 A schematic diagram of the integral area of ​​an aircraft toward an offshore drilling platform area D provided in an embodiment of the present application. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0024] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0025] The present invention provides a method for calculating the probability of a two-dimensional standard normal distribution, including:

[0026] Step 101: Select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value.

[0027] Step 102: Integrate the horizontal axis variable and construct a function using Taylor's formula and integration by parts method; wherein the constructed function is used to approximate the original function of the one-dimensional standard normal distribution density function.

[0028] Step 103: Based on the constructed function, the two-dimensional standard normal distribution probability calculation problem is converted into a curve integral problem for the ordinate variable, and the approximate value of the curve integral of the ordinate variable is calculated on each directed arc segment.

[0029] Step 104: Determine the two-dimensional standard normal distribution probability based on the approximate value of the curve integral of the ordinate variables on all directed arc segments.

[0030] In an exemplary embodiment, according to the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments, specifically comprising: based on the y-axis step length h y , the key nodes of the integral region boundary curve, or the insertion points between two adjacent key nodes on the positive boundary curve, are arranged in sequence along the positive boundary curve to generate a segmentation point sequence; the positive boundary curve is divided into a plurality of directed arc segments according to the segmentation point sequence; the ordinate variables on the directed arc segments monotonically increase or monotonically decrease, and the direction of the directed arc segments is consistent with the positive direction of the positive boundary curve.

[0031] Furthermore, the input precision ε, ε>10 -7 , y-axis step length h y =2, select approximation The order of the Taylor polynomial is 2m, and the appropriate x-axis step length h is selected x ,satisfy

[0032]

[0033] Select the point A on the positive boundary curve L of the integration region i (x i ,y i )(i=1,2,...,l), A1 is the key node, A i (i=2,3,…,l) is a key node or an insertion point between two adjacent key nodes on the positive boundary curve, and is arranged in sequence along the positive boundary curve. l+1 =A1. Point A i (x i ,y i )(i=1,2,...,l) splits the positive boundary curve L into l directed arc segments, Directed arc The upper ordinate increases or decreases monotonically and its direction is consistent with the positive direction of the boundary curve.i+1 -y i |≤h y ,i=1,2,…,l。 Usually when choosing the split point|y i+1 -y i | is as large as possible, so that the number of directed arc segments l after segmentation is as small as possible. The number of directed arc segments l is determined by the above segmentation process.

[0034] In an exemplary embodiment, the constructed function P x (x) is:

[0035]

[0036] Among them, h x is the x-axis step length; t is the integral variable; k x For not more than The maximum integer of , using the complex Simpson formula to calculate the probability of meeting the accuracy requirements

[0037]

[0038] The symbolic function sgn(x) is defined as:

[0039]

[0040] H is the upper (ε / 4) quantile, that is:

[0041]

[0042] In an exemplary embodiment, the directed arcs are calculated The approximate value Q of the curve integral about the coordinate y i :

[0043]

[0044] Where i is the number of the directed arc segment; j is the number of the weight coefficient; x=f(y) represents the equation of the integral curve, ω j is the interpolation point y i(2j-1) and i(2j) The weight coefficients at the points are calculated using the following formula:

[0045]

[0046] P x (f(y i(2j) ))、P x (f(y i(2j-1) )) respectively represent the function P constructed by formula (2) x (x) when the variable x takes the value of f(y i(2j))、f(y i(2j-1) ), f(y i(2j) )、f(y i(2j-1) ) represent the interpolation points y i(2j) ,y i(2j-1) The value of the x coordinate at .

[0047] Compute an approximation to the probability of a two-dimensional standard normal distribution over an integration region:

[0048]

[0049] The present application realizes the automation of numerical calculation of the probability of two-dimensional standard normal distribution on complex integral regions, constructs an approximate function that meets the accuracy requirements, transforms the problem of calculating the probability of two-dimensional standard normal distribution into a curve integral of coordinates, and uses a high-precision numerical integration method to calculate the curve integral in sections to obtain the probability of two-dimensional standard normal distribution, thus overcoming the problems of low integration accuracy and excessive numerical calculation caused by the shape of the integral region.

[0050] In addition, when calculating multiple two-dimensional normal distribution probabilities on an integral region, the advantages of the present application are particularly obvious. The two-dimensional standard normal distribution probability obtained after the substitution method only needs to be calculated according to formula (8), without the need to repeatedly split the integral curve or repeatedly calculate

[0051] The present application also provides an application scenario. Taking the problem of "normal distribution probability calculation when an aircraft drops equipment maintenance spare parts to area D of an offshore drilling platform" as an example, the application scenario applies the above-mentioned two-dimensional standard normal distribution probability numerical calculation method.

[0052] Use an airplane to drop equipment maintenance spare parts on the offshore drilling platform area D. Take the center of the airplane as the origin and the airplane's centerline as the x-axis to establish a coordinate system. Affected by the climate, the drop points of equipment maintenance spare parts on the platform follow a two-dimensional standard normal distribution. Calculate the probability of a two-dimensional standard normal distribution on the platform area D The coordinates of the key nodes on the positive boundary curve of the integral region are shown in Table 1. The integral region of the aircraft to the offshore drilling platform region D is shown in Figure 2 As shown, the curve is in the ellipse and straight line segments, with an accuracy of ε = 10 -5 .

[0053] Table 1 Coordinates of key nodes on the positive boundary curve of the integration region

[0054] Serial number k 1 2 3 4 5 <![CDATA[(x k ,and k )]]> (8,3) (4,3) (4,6) (0,3) (4,0)

[0055] Based on the conditions in the problem, calculate the probability of a two-dimensional standard normal distribution.

[0056] Step 201: Segment the positive boundary curve of a given integral region in actual requirements into a plurality of directed arc segments.

[0057] Step 2011: Input precision ε (ε>10 -7 ), y-axis step length h y =2, select approximation The order of the Taylor polynomial is 2m = 6, and the x-axis step size h is selected x =0.5, satisfying

[0058]

[0059] Step 2012: Select a point A on the positive boundary curve L of the integration region i (x i ,y i )(i=1,2,...,l),l=9, as shown in Table 2, the positive boundary curve L is divided into l directed arc segments, A l+1 =A1, directed arc The upper ordinate increases or decreases monotonically, and |y i+1 -y i |≤h y ,i=1,2,…,l。

[0060] Table 2. Points on the positive boundary curve of the integral region

[0061]

[0062] Step 202: Constructor:

[0063]

[0064] in, The probability of meeting the accuracy requirement is calculated using the complex Simpson formula

[0065]

[0066] Different k x Corresponding probability As shown in Table 3:

[0067] Table 3 Different k x Corresponding probability

[0068]

[0069] The symbolic function sgn(x) is defined as:

[0070]

[0071] H is the upper quantile, and H=4.5648 satisfies:

[0072]

[0073] Step 203: Calculate the two-dimensional standard normal distribution probability on the integration region.

[0074] Step 2031: Calculate directed arc segments The approximate value Q of the curve integral about the coordinate y i :

[0075]

[0076] Where x = f(y) represents the arc segment of the integral curve The equation, ω j ,y ij Represent weight coefficients and interpolation points respectively:

[0077] (ω j )=(0.1012285,0.2223810,0.3137066,0.3626838)

[0078]

[0079] P x (f(y i(2j) ))、P x (f(y i(2j-1) )) respectively represent the function P constructed by formula (2) x (x) when the variable x takes the value of f(y i(2j) )、f(y i(2j-1) ), f(y i(2j) )、f(y i(2j-1) ) represent the interpolation points y i(2j) ,y i(2j-1) The value of the x coordinate at .

[0080] Step 2032: Calculate the probability of the two-dimensional standard normal distribution on the integration area:

[0081]

[0082] Output the calculation results and exit the calculation.

[0083] According to step 203, the probability in the integral region is obtained as P=0.06072.

[0084] For the problem of "calculating the normal distribution probability when an aircraft drops equipment maintenance spare parts to offshore drilling platform area D", the ultimate goal is to find the best drop point through calculation so that when an aircraft drops equipment maintenance spare parts to offshore drilling platform area D, the probability of the spare parts being dropped on the drilling platform area is maximized.

[0085] Furthermore, for the same accuracy ε, a smaller step size h is usually chosen. x , then the probability of saving can improve computational efficiency; therefore, P x (x) can be calculated by integration by parts, with a step size of h x When P is smaller x (x) expression will be simpler, and P can be reduced accordingly. x (x) The amount of calculation required. Obviously, the value of the constructed function is calculated x (x), the amount of calculation required to directly use the complex Simpson method each time is greater than that required by formula (2), and it contains a large number of repeated calculations, which reduces the calculation efficiency.

[0086] When calculating the probability of a two-dimensional standard normal distribution on different integral regions, it is only necessary to segment the boundary curve of the integral region as required, and using formula (6) and formula (8), the two-dimensional standard normal distribution probability calculation problem is converted into a one-dimensional numerical integration problem that can be calculated by the Gauss-Legendre integral formula. When calculating the probability of a two-dimensional normal distribution with the same standard deviation but different means on the same integral region, the segmentation of the boundary curve of the integral region does not change. Using the double integral substitution method, the two-dimensional normal distribution probability calculation problem can be converted into the two-dimensional standard normal distribution probability calculation problem. The approximate calculation formula obtained by formula (2) only needs to be calculated once, and the positive boundary curve of the integral region only needs to be segmented once. The present invention uses Taylor's formula, Gauss-Legendre integral formula and complex Simpson's formula to convert the two-dimensional standard normal distribution probability calculation problem into a relatively simple one-dimensional numerical calculation problem, with high calculation accuracy and fast solution speed. It is a good method for quickly calculating the probability of a two-dimensional normal distribution on a complex integral region. For the calculation problem of the probability of a two-dimensional normal distribution with the same standard deviation on the same integral region, since the positive boundary curve of the integral region only needs to be segmented once, the amount of calculation can be reduced.

[0087] Based on the same inventive concept, the embodiment of the present application also provides a two-dimensional standard normal distribution probability numerical calculation device for implementing the two-dimensional standard normal distribution probability numerical calculation method involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in one or more two-dimensional standard normal distribution probability numerical calculation device embodiments provided below can refer to the limitations of the two-dimensional standard normal distribution probability numerical calculation method above, and will not be repeated here.

[0088] In an exemplary embodiment, a two-dimensional standard normal distribution probability numerical calculation device is provided, comprising:

[0089] Segmentation module, used to select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value.

[0090] Function construction module, used to integrate the horizontal axis variables and construct functions using Taylor's formula and integration by parts method.

[0091] The approximate value calculation module of the curve integral is used to convert the two-dimensional standard normal distribution probability calculation problem into the curve integral problem of the ordinate variable based on the constructed function, and calculate the approximate value of the curve integral of the ordinate variable on each directed arc segment.

[0092] The two-dimensional standard normal distribution probability determination module is used to determine the two-dimensional standard normal distribution probability according to the approximate value of the curve integral of the ordinate variable on all directed arc segments.

[0093] In an exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O for short) and a communication interface. The processor, the memory and the input / output interface are connected via a system bus, and the communication interface is connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store two-dimensional standard normal distribution probability numerical calculation data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a two-dimensional standard normal distribution probability numerical calculation method is implemented.

[0094] In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0095] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0096] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0097] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0098] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ReadOnlyMemory, ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (Magnetoresistive RandomAccess Memory, MRAM), ferroelectric random access memory (Ferroelectric RandomAccess Memory, FRAM), phase change memory (Phase Change Memory, PCM), graphene memory, etc. Volatile memory can include random access memory (RandomAccess Memory, RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0099] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0100] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0101] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A two-dimensional standard normal distribution probability numerical calculation method, characterized in that: The two-dimensional standard normal distribution probability numerical calculation method comprises: Select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value; Integrate the abscissa variable and construct the function using Taylor's formula and integration by parts; Based on the constructed function, the probability calculation problem of the two-dimensional standard normal distribution is converted into a curve integral problem of the ordinate variable, and the approximate value of the curve integral of the ordinate variable is calculated on each directed arc segment; Determine the two-dimensional standard normal distribution probability based on the approximation of the curve integral of the ordinate variable over all directed arc segments.

2. The two-dimensional standard normal distribution probability numerical calculation method according to claim 1 is characterized in that: According to the key nodes of the positive boundary curve of the integration area and the y-axis step size h y The positive boundary curve is divided into a plurality of directed arc segments, specifically comprising: Based on the y-axis step length h y , arranging the key nodes of the integral region boundary curve, or the insertion points between two adjacent key nodes on the positive boundary curve, in sequence along the positive boundary curve to generate a segmentation point sequence; The positive boundary curve is divided into a plurality of directed arc segments according to the segmentation point sequence; the ordinate variables on the directed arc segments increase or decrease monotonically, and the directions of the directed arc segments are consistent with the positive direction of the positive boundary curve.

3. The two-dimensional standard normal distribution probability numerical calculation method according to claim 2 is characterized in that: x-axis step length h x and the y-axis step length h y The following conditions are met: Y-axis step length h y =2; Among them, ε is the accuracy requirement; 2m is The order of the Taylor polynomial of , where x is the horizontal axis variable.

4. The two-dimensional standard normal distribution probability numerical calculation method according to claim 1 is characterized in that: The constructed function P x (x) is: Among them, sgn(x) is the sign function; x is the horizontal coordinate variable; is the probability of meeting the accuracy requirement; k x For not more than The largest integer; h x is the x-axis step length; t is the integral variable; 2m is is the order of the Taylor polynomial; H is the upper (ε / 4) quantile.

5. The two-dimensional standard normal distribution probability numerical calculation method according to claim 1 is characterized in that: The approximate value Q of the curve integral of the ordinate variable i for: Among them, i is the serial number of the directed arc segment; j is the serial number of the weight coefficient; ω j is the interpolation point y i(2j-1) and interpolation point y i(2j) The weight coefficient; x = f (y) represents the equation of the integral curve; P x (f(y i(2j) )) and P x (f(y i(2j-1) )) are the constructed functions P x (x) when the variable x takes the value of f(y i(2j) )、f(y i(2j-1) ) when f(y i(2j) ) and f(y i(2j-1) ) represent the interpolation points y i(2j) and interpolation point y i(2j-1) The value of the horizontal axis variable x at .

6. The two-dimensional standard normal distribution probability numerical calculation method according to claim 5 is characterized in that: The two-dimensional standard normal distribution probability P is: Where l is the total number of directed arcs.

7. A two-dimensional standard normal distribution probability numerical calculation device, characterized in that: The dimensional standard normal distribution probability numerical calculation device comprises: Segmentation module, used to select the x-axis step length h according to the accuracy requirements x and the y-axis step length h y , and based on the key nodes of the positive boundary curve of the integration region and the y-axis step length h y The positive boundary curve is divided into a plurality of directed arc segments; the key nodes include the vertices of the polygon, the corresponding points of the curve's abscissa extreme value and the corresponding points of the ordinate extreme value; Function construction module, used to integrate the horizontal axis variable and construct functions using Taylor's formula and integration by parts method; The approximate value calculation module of the curve integral is used to convert the probability calculation problem of the two-dimensional standard normal distribution into the curve integral problem of the ordinate variable based on the constructed function, and calculate the approximate value of the curve integral of the ordinate variable on each directed arc segment; The two-dimensional standard normal distribution probability determination module is used to determine the two-dimensional standard normal distribution probability according to the approximate value of the curve integral of the ordinate variable on all directed arc segments.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the two-dimensional standard normal distribution probability numerical calculation method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the two-dimensional standard normal distribution probability numerical calculation method described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the two-dimensional standard normal distribution probability numerical calculation method described in any one of claims 1 to 6 is implemented.

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