Mixture Distribution Statistics Computation via Segmented Moments

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Solution Overview

Problem

Computing accurate statistics for mixture distributions in large sample populations is computationally and memory-intensive, leading to inaccurate aggregate mean and variance calculations, particularly in wireless systems using the Irregular Terrain Model (ITM) for path loss modeling.

Innovation Solution

A method that determines the median, parent mean, parent standard deviation, and segment boundaries for mixture distributions, using scaled probabilities and segment moments to compute mixture mean and variance, reducing the need for raw power measurement samples and minimizing computational and memory resources.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If large sample populations are used to compute mean and variance of mixture distributions, then measurement precision is improved, but device complexity and computation overhead increase

Engineering Contradiction:

Improveaccuracy of estimated mean and varianceVSAvoidmemory and computation overhead

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The mixture distribution is divided into multiple segments, each representing a different component distribution. By computing statistics for each segment separately and then combining them using scaled probabilities, the method avoids the need to process large sample populations for the entire mixture distribution, thereby reducing memory and computation overhead while maintaining accuracy

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The method extracts and computes statistics for individual segments of the mixture distribution rather than processing the complete mixture distribution with large sample populations. This extraction approach allows for more efficient computation by focusing on smaller, manageable segments that can be processed with reduced computational resources

Inventive Principle:

Principle #2Taking out (Extraction)

2Productivity

If individual mean and variance errors are accumulated when computing the mean of the sum of multiple distributions, then computation is simplified, but measurement precision deteriorates

Engineering Contradiction:

Improvecomputation efficiencyVSAvoidaccuracy of aggregate mean and variance

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The method introduces scaled probabilities as intermediary weights when combining segment statistics. By using these scaled probabilities to compute the aggregate mean and variance, the method accurately accounts for the contribution of each segment while maintaining computational efficiency, avoiding the error accumulation that would occur with simple addition of individual statistics

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS11204978B2Computing statistics for mixture distributions

Publication Date: 2021.12.21 OUTDOOR WIRELESS NETWORKS LLC

AI summary

A computing device includes a processor and memory storing instructions that are executable to determine a median of a first mixture distribution. The instructions are also executable to determine a parent mean, a parent standard deviation, and boundaries for each of multiple segments in the first mixture distribution. The instructions are also executable to determine a segment mean and a segment second moment for each segment based on the parent mean, the parent standard deviation, and the boundaries for the respective segment. The instructions are also executable to determine a scaled probability for each segment. The instructions are also executable to determine a mixture mean and a mixture standard deviation for the first mixture distribution based on the segment mean, the segment second moment, and the scaled probability for each segment in the first mixture distribution.