Death probability measuring and calculating system and method

Abstract

The invention relates to the technical field of population prediction, in particular to a death probability measuring and calculating system and method. The system comprises a data acquisition module, a prediction module and a display module, the data acquisition module is used for acquiring death related data of a certain region, and the prediction module is used for providing a Kannisto death prediction model, a Lee-Carter death prediction model and a Brass death prediction model to predict death data of the certain region through the acquired death related data. The display module is used for arranging and displaying the predicted death data of the certain region; according to the invention, three death prediction models are provided to measure and calculate the death probability of a certain region, and the death population of a certain region in a future time period can be predicted based on the obtained death probability, so that the population prediction of a certain region is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of population prediction, and in particular to a death probability estimation system and method. Background Art

[0002] my country is a country with a large population. According to the National Bureau of Statistics, the total population of my country will be 1409.67 million by the end of 2023, with 11.1 million deaths, of which 296.97 million are over 60 years old, accounting for 21.1% of the total population. Therefore, studying the probability of death of the population, especially the probability of death of the elderly, is a very important research direction.

[0003] With the development of society and the advancement of science and technology, the collection and management of death data has become an important task in many fields such as public health, insurance actuarial science, and demography. However, the existing methods for calculating the probability of death often have certain limitations, such as complex operation, low calculation efficiency, and low accuracy. These problems limit the effective use of death data and the application of death probability calculation technology in practical work. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention aims to provide a death probability calculation system and method to solve the problems of low calculation efficiency and low accuracy existing in the death probability calculation technology.

[0005] In order to solve the above problems, the present invention adopts the following technical solutions:

[0006] In one aspect, the present invention provides a death probability estimation system, comprising a data acquisition module, a prediction module and a display module;

[0007] The data acquisition module is used to acquire death-related data in a certain area;

[0008] The prediction module is used to provide the Kannisto death prediction model, the Lee-Carter death prediction model and the Brass death prediction model to predict the death data of a certain area through the acquired death-related data;

[0009] The display module is used to organize and display the predicted death data of a certain area.

[0010] As an implementable method, the death-related data include the population by age, the number of deaths by age, the cumulative number of survival person-years by age, and the number of survivors by age.

[0011] As an implementation method, the Kannisto death prediction model calculates the probability of death by the following formula: :

[0012]

[0013] Among them, x is the input death-related data, α and β are the parameters to be estimated;

[0014] Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method.

[0015] As an implementable method, the Lee-Carter death prediction model predicts death data of a certain area by acquiring death-related data, including:

[0016] Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of

[0017] The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time;

[0018] make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution :

[0019]

[0020] Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x;

[0021] The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ;

[0022] but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence;

[0023] pass calculate .

[0024] As an implementable embodiment, the Brass death prediction model is ,in , select three sets of life table data, extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, they are a1, b1 and a2, b2 respectively, record:

[0025] , , ;

[0026] in, , Represents two sets of life tables, represents the basic standard life table, x represents the age group;

[0027] but , ;

[0028] Note the result variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get:

[0029]

[0030]

[0031]

[0032] ;

[0033] according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick :

[0034]

[0035] After finding the coefficients, we can then find , , Pick :

[0036] Assume that from the standard year to fit a1, b1 and a2, b2 after n years of change, use two points to fit the future , : , , and the predicted year , ;

[0037] according to , calculate the forecast year :From the equation Available , and simplify it to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

[0038] In another aspect, the present invention provides a method for calculating the probability of death, comprising:

[0039] Get death-related data for a certain area;

[0040] The Kannisto death prediction model, Lee-Carter death prediction model and Brass death prediction model are used to predict the death data of a certain area through the death-related data obtained;

[0041] The predicted death data for a certain area is collated and displayed.

[0042] As an implementable method, the death-related data include the population by age, the number of deaths by age, the cumulative number of survival person-years by age, and the number of survivors by age.

[0043] As an implementation method, the Kannisto death prediction model calculates the probability of death by the following formula: :

[0044]

[0045] Among them, x is the input death-related data, α and β are the parameters to be estimated;

[0046] Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method.

[0047] As an implementable method, the method of using the Lee-Carter death prediction model to predict death data in a certain area by using the acquired death-related data includes:

[0048] Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of

[0049] The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time;

[0050] make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution :

[0051]

[0052] Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x;

[0053] The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ;

[0054] but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence;

[0055] pass calculate .

[0056] As an implementable embodiment, the Brass death prediction model is ,in , select three sets of life table data, extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, they are a1, b1 and a2, b2 respectively, record:

[0057] , , ;

[0058] in, , represents two sets of life tables, represents the basic standard life table, x represents the age group;

[0059] but , ;

[0060] Note the outcome variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get:

[0061]

[0062]

[0063]

[0064] ;

[0065] according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick :

[0066]

[0067] After finding the coefficients, we can then find , , Pick :

[0068] Assume that from the standard year to fit a1, b1 and a2, b2 after n years of change, use two points to fit the future , : , , and the predicted year , ;

[0069] according to , calculate the forecast year :From the equation Available , and simplify it to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

[0070] The beneficial effect of the present invention is that the present invention provides three death prediction models to calculate the death probability of a certain area. Based on the obtained death probability, the death population of a certain area in a future time period can be predicted, thereby realizing fast and accurate population prediction of a certain area. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 Schematic diagram of a death probability calculation system in an embodiment of the present invention.

[0072] Figure 2 The figure is a flow chart of a method for calculating the probability of death in an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The present invention is further described in detail below in conjunction with specific embodiments.

[0074] It should be noted that these embodiments are only used to illustrate the present invention rather than to limit the present invention. Simple improvements to the method based on the concept of the present invention all fall within the scope of protection claimed by the present invention.

[0075] See also Figure 1 , is a death probability estimation system, comprising a data acquisition module 100, a prediction module 200 and a display module 300;

[0076] The data acquisition module 100 is used to acquire death-related data in a certain area.

[0077] Among them, death-related data include but are not limited to the population by age, the number of deaths by age, the cumulative number of survival person-years by age, and the number of survivors by age.

[0078] The system also includes a web client for users to fill in data templates according to data required for prediction. The web client transmits the collected death-related data to the data acquisition module and the prediction module.

[0079] The prediction module 200 is used to provide the Kannisto death prediction model, the Lee-Carter death prediction model and the Brass death prediction model to predict the death data of a certain area by using the acquired death-related data.

[0080] Users can choose the death prediction model to use according to calculation needs, or they can choose different models for prediction, including the Kannisto death prediction model, the Lee-Carter death prediction model, and the Brass death prediction model. Then they can compare the results and select relatively good prediction result data.

[0081] Among them, the Kannisto death prediction model calculates the probability of death by the following formula: :

[0082]

[0083] Among them, x is the input death-related data, α and β are the parameters to be estimated;

[0084] Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method. The historical death probability Qx = Mx / (1+0.5Mx), where Mx is the historical mortality rate.

[0085] Among them, the Lee-Carter death prediction model predicts the death data of a certain area by obtaining death-related data, including:

[0086] Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of

[0087] The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time;

[0088] make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution :

[0089]

[0090] Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x;

[0091] The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ;

[0092] but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence, converting the new sequence substitution ;

[0093] pass calculate .

[0094] Among them, the Brass death prediction model is ,

[0095] in , select three sets of life table data (the three sets of life tables refer to three life tables with different life expectancies, consisting of age, death probability, number of deaths, number of survivors, total number of survivors, and age-specific life expectancy), and extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, they are a1, b1 and a2, b2 respectively, record:

[0096] , , ;

[0097] Among them, logit() is the logistic regression function, , represents two sets of life tables, Standard life tables representing the basis;

[0098] in, , represents two sets of life tables, represents the basic standard life table, x represents the age group;

[0099] but , ;

[0100] Note the outcome variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get:

[0101]

[0102]

[0103]

[0104] ;

[0105] according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick :

[0106]

[0107] Find the coefficient Then find , , Pick :

[0108] Assume that from the standard year to fit a1, b1 and a2, b2 after n years of change, use two points to fit the future , : , , and the predicted year , ;

[0109] according to , calculate the forecast year :From the equation Available , simplifying to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

[0110] The display module 300 is used to organize and display the predicted death data of a certain area.

[0111] Through the display module, users can see the results of this prediction, including the probability of death in future years and by age. This module displays the results in the form of charts, etc. Users can download the corresponding data and pictures as needed.

[0112] See also Figure 2 , which is a method for calculating the probability of death, including:

[0113] S100, obtaining death-related data of a certain region. Death-related data include but are not limited to the number of people by age, the number of deaths by age, the cumulative number of survival years by age, and the number of survivors by age. A web client may also be provided to allow users to fill in a data template according to the data required for prediction.

[0114] S200 provides Kannisto death prediction model, Lee-Carter death prediction model and Brass death prediction model to predict the death data of a certain area by obtaining death-related data.

[0115] Users can choose the death prediction model to use according to calculation needs, or they can choose different models for prediction, including the Kannisto death prediction model, the Lee-Carter death prediction model, and the Brass death prediction model. Then they can compare the results and select relatively good prediction result data.

[0116] Among them, the Kannisto death prediction model calculates the probability of death by the following formula: :

[0117]

[0118] Among them, x is the input death-related data, α and β are the parameters to be estimated;

[0119] Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method.

[0120] Among them, the Lee-Carter death prediction model predicts the death data of a certain area by obtaining death-related data, including:

[0121] Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of

[0122] The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time;

[0123] make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution :

[0124]

[0125] Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x;

[0126] The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ;

[0127] but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence;

[0128] pass calculate .

[0129] Among them, the Brass death prediction model is ,

[0130] in , select three sets of life table data (the three sets of life tables refer to three life tables with different life expectancies, consisting of age, death probability, number of deaths, number of survivors, total number of survivors, and age-specific life expectancy), and extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, they are a1, b1 and a2, b2 respectively, record:

[0131] , , ;

[0132] in, , represents two sets of life tables, represents the basic standard life table, x represents the age group;

[0133] but , ;

[0134] Note the outcome variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get:

[0135]

[0136]

[0137]

[0138] ;

[0139] according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick :

[0140]

[0141] After finding the coefficients, we can then find , , Pick :

[0142] Assume that from the standard year to fit a1, b1 and a2, b2 after n years of change, use two points to fit the future , : , , and the predicted year , ;

[0143] according to , calculate the forecast year :From the equation Available , and simplify it to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

[0144] S300. Arrange and display the predicted death data of a certain area.

[0145] Through the display module, users can see the results of this prediction, including the probability of death in future years and by age. This module displays the results in the form of charts, etc. Users can download the corresponding data and pictures as needed.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described with reference to the preferred embodiments of the present invention, it should be understood by those skilled in the art that various changes may be made in form and details without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A death probability calculation system, It is characterized in that It includes data acquisition module, prediction module and display module; The data acquisition module is used to acquire death-related data in a certain area; The prediction module is used to provide the Kannisto death prediction model, the Lee-Carter death prediction model and the Brass death prediction model to predict the death data of a certain area through the acquired death-related data; The display module is used to organize and display the predicted death data of a certain area.

2. The death probability calculation system according to claim 1, It is characterized in that The death-related data include the population by age, the number of deaths by age, the cumulative number of survival person-years by age and the number of survivors by age.

3. The death probability calculation system according to claim 1, It is characterized in that The Kannisto death prediction model calculates the probability of death by the following formula : Among them, x is the input death-related data, α and β are the parameters to be estimated; Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method.

4. The death probability calculation system according to claim 1, It is characterized in that The Lee-Carter death prediction model predicts the death data of a certain area by acquiring death-related data, including: Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time; make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution : Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x; The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ; but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence; pass calculate .

5. The death probability calculation system according to claim 1, It is characterized in that The Brass death prediction model is ,in , select three sets of life table data, extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, respectively 1 , b 1 and a 2 , b 2 ,remember: ， ， ； in, , Represents two sets of life tables, represents the basic standard life table, x represents age; but , ; Note the result variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get: ； according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick : After finding the coefficients, we can then find , , Pick : Assume that from the standard year to the fitting a 1 , b 1 and a 2 , b 2 After n years of changes, two points are used to predict the future , : , , and the predicted year , ; according to , calculate the forecast year :From the equation Available , and simplify it to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

6. A method for calculating the probability of death, It is characterized in that include: Get death-related data for a certain area; The Kannisto death prediction model, Lee-Carter death prediction model and Brass death prediction model are used to predict the death data of a certain area through the death-related data obtained; The predicted death data for a certain area is collated and displayed.

7. The method for calculating the probability of death according to claim 6, It is characterized in that The death-related data include the population by age, the number of deaths by age, the cumulative number of survival person-years by age and the number of survivors by age.

8. The method for calculating the probability of death according to claim 6, It is characterized in that The Kannisto death prediction model calculates the probability of death by the following formula : Among them, x is the input death-related data, α and β are the parameters to be estimated; Will Simplify, we get ,in The historical death probability corresponding to the input historical death-related data is calculated, and α and β are calculated using the least squares method.

9. The method for calculating the probability of death according to claim 6, It is characterized in that The Lee-Carter death prediction model is used to predict the death data of a certain area by obtaining death-related data, including: Let the logarithmic mortality rate obey ,in, , The age-specific mortality rate is is the sensitivity of the corresponding age group to the mortality rate change rate, is the rate of change of mortality over time, is the error term, which has a mean of 0 and a variance of Normal distribution of The mortality rate is decomposed into three parts, including the basic age-specific mortality rate, the fluctuation of age-specific mortality rate and the change of mortality rate over time; make as well as , the error term is calculated by assuming that the mortality rate follows a Poisson distribution : Each Take the logarithm, take ,in is the starting year, T is the ending year, h is the total number of years, k is the number of age groups, is a column vector of the average mortality rate for age group x, is the column vector of age-specific mortality rates for age group x; The matrix Perform singular value decomposition and we get ,in, is an orthogonal matrix with x rows and x columns, is an orthogonal matrix with t rows and t columns, Q is a diagonal matrix with the singular values ​​of A as diagonals and the rest of the values ​​​​as 0; arrange the singular values ​​of A from large to small and take the largest singular value , and take its corresponding left vector and right vector ; but , , is the sum of each element of the column vector; use Model: , it is estimated that , and calculate the new sequence; pass calculate .

10. The method for calculating the probability of death according to claim 6, It is characterized in that The Brass death prediction model is ,in , select three sets of life table data, extract the survival probability function data from one set of life table data, defined as , as the standard; the survival probability function data are extracted from the other two sets of life table data, both defined as , using the least squares method to fit the coefficients a and b, respectively 1 , b 1 and a 2 , b 2 ,remember: ， ， ； in, , Represents two sets of life tables, represents the basic standard life table, x represents the age group; but , ; Note the result variable , calculate partial derivatives of a and b respectively, set the partial derivatives to zero, and we get: ； according to The least squares method is used to fit the prediction Least squares fitting to find the predicted ,make , Pick , Pick , using the least squares method to find , then find , , Pick : After finding the coefficients, we can then find , , Pick : Assume that from the standard year to the fitting a 1 , b 1 and a 2 , b 2 After n years of changes, two points are used to predict the future , : , , and the predicted year , ; according to , calculate the forecast year :From the equation Available , and simplify it to get: ,pass Calculating survivor years , calculate the number of deaths : , the probability of death is obtained, For the population.

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