3 min read
Mixed Poisson Distribution With An Inverse Gaussian
The content provided is a mathematical derivation showing that a mixed Poisson distribution with an inverse Gaussian mixing distribution is equivalent to a Poisson-ETNB distribution.
Statistics
11 posts
2 min read
Inequality Around sum of the cubics and AM-GM variance
The given text consists of two parts. The first part contains two examples along with their proofs concerning inequalities. In the first example, it is proved that if 'a_i' are real numbers such that the sum of their squares, the summation of (a_i^2), is less than or equal to 4, then the sum of their cubes, the summation of (a_i^3), will be less than or equal to 8. The proof involves utilizing the AM-GM inequality to demonstrate that the sum of the cubes is bounded by 8. In the second example, an inequality is proved for non-negative numbers 'a', 'b', and 'c': a^3 + b^3 + c^3 - 3abc is greater than or equal to 2((b+c)/2 - a)^3.
7 min read
Introduction to different moments of distributions (Planned)
We will get into how to get different moments of different distributions and possible skewness and kurtosis of different distributions. We will also discuss the relationship between different moments and the moment generating function.
16 min read
A Brief Introduction to Compound Distributions (Part One)
The provided text discusses the concept of compound distributions, which arise when combining two independent distributions. The probability generating function (pgf) of a compound distribution is shown to be the composition of the pgfs of the primary and secondary distributions. Some of the examples are excerpted from Loss Model (Sixth Edition).
21 min read
A Brief Introduction to Point Estimates
In this blog, We introduces various methods in point estimates and their definition. The blog follows from lecture note Point Estimate from professor Xiaojing Ye in Georgia State University
14 min read
Notes on Life Insurance (Part One)
The text primarily covers actuarial formulas and concepts related to life insurance and financial mathematics, providing insights into the calculation of present values and probabilities for different scenarios. keywords: Makeham's Law, Interest and Discount Formulas, Actuarial Present Value, Variance of Payments, Whole Life Annuity, Deferred Insurance, Relations among Different Present Values, Decomposition of Term Insurance
6 min read
Notes on Life Insurance (Part Two)
The text also mentions exercises based on actuarial mathematics for life contingent risks, which involve calculating EPVs and variance of benefits. Keywords: indicator variable, EPV Formulas, term insurance and whole life insurance, geometric payout.
21 min read
Understanding Discrete Distributions and Their Applications in Actuarial Science
In this blog, We introduces various discrete distributions and discusses their properties, particularly focusing on the counting distribution, Poisson distribution, negative binomial distribution, and binomial distribution. Counting Distribution, Poisson Distribution, Negative Binomial Distribution, Memoryless Property, Binomial Distribution, The (a,b,0)-Class
5 min read
Couple exercises from Sampling Distributions (Part One)
Statistics and Sample Properties, Sampling Distribution of the Mean, Chebyshev's Inequality, Weak Law of Large Numbers (WLLN), Central Limit Theorem (CLT), Sample Distribution with Finite Population and Without Replacement.
10 min read
Couple exercises from Sampling Distributions (Part Two)
Chi-squared Distribution, Student's t-distribution, Fisher's F-distribution, Order Statistics.
6 min read
Couple exercises from Functions of Random Variables
Examples include finding the probability density functions of transformed random variables, absolute values, sums of independent variables, and squared variables, as well as obtaining the cumulative distribution function, applying the moment generating function theorem, and determining the distributions of sums of Poisson and exponential random variables.