# Recent probability posts

### Minimum Bias and Exponential Family Distributions

2020-10-20 | probability, minimum bias, glm, exponential family

Introduction This post introduces four short expository notes describing exponential family distributions that are often used to model insurance losses. The exponential family underlies generalized linear models (GLMs), a

### Probability Models for Insurance Losses

2020-10-20 | probability, minimum bias, glm, exponential family

Part III of a four part series “Minimum Bias and Exponential Family Distributions”.

### Modes of Convergence

2022-01-20 | mathematics, probability

Random variables can converge in several different ways. Here is a brief introduction, highlighting examples of the different behaviors that can occur. Many of the examples below are taken from

### The Tweedie Power Variance Function Family

2020-10-20 | probability, minimum bias, glm, exponential family

Part IV of a four part series “Minimum Bias and Exponential Family Distributions”.

### Exponential Family Distributions

2020-10-20 | probability, minimum bias, glm, exponential family

Part II of a four part series “Minimum Bias and Exponential Family Distributions”.

### Bailey Simon Minimum Bias Reexamined

2020-10-20 | probability, minimum bias, glm, exponential family

Part I of a four part series “Minimum Bias and Exponential Family Distributions”.

### Frequency Distributions

2018-09-15 | probability, distribution, frequency, mixed

A random variable $$N$$ is $$G$$-mixed Poisson if $$N\mid G$$ has a Poisson $$nG$$ distribution for some fixed non-negative $$n$$ and a non-negative mixing

### The Power Variance Family of Distributions

2022-01-28 | presentations, writing, statistics, probability