Statistics How To

< Probability Distributions > Exponential Distribution Contents: What is an Exponential Distribution? What is a Poisson Process? Uses in real life Memoryless Property Exponential PDF Exponential CDF Connection to other distributions Exponential Family Linear Exponential Distribution What is an Exponential distribution?     The exponential distribution, frequently used in reliability tests, describes time between events … Read more

< Probability Distributions > Beta Distribution Contents: What is a Beta Distribution? Properties Software Options: Mathematica and R Excel Beta Distribution: BETA.DIST & INV.BETA Applications of the Beta Density Function What is a Beta Distribution? The beta distribution (also called the beta distribution of the first kind) is a family of continuous probability distributions defined on … Read more

Non Normal Distributions > Inverse Gamma Distribution What is the Inverse Gamma Distribution? The inverse gamma distribution (or inverted gamma distribution) is commonly used for Bayesian analysis. It has the same distribution of the reciprocal of the gamma distribution. The inverse chi-squared is a special case of the inverse gamma distribution with α = ν /2 … Read more

Probability Distributions > Bell-Shaped Distribution What is a bell shaped distribution? A bell-shaped distribution is – perhaps not surprisingly – any distribution that looks like the shape of a bell when plotted as a graph. These distributions have one mode (or peak), the mean is close to the median, and the majority of data points … Read more

Probability Distributions > Bates Distribution What is the Bates Distribution? The Bates Distribution (or rectangular mean distribution) is a probability distribution of the mean of a number of independent uniformly distributed random variables on the unit interval [1]. The distribution resembles can look like several other distributions depending on how many items are in the sample. For larger … Read more

Probability Distributions > Benford distribution What is the Benford Distribution? The Benford distribution, denoted X ∼ Benford, describes the distribution of random variables that follows Benford’s law.  Benford’s law (also called the first digit law) states that the first (non-zero) digit (i.e., the digits 1 to 9) in a wide range of number collections doesn’t … Read more

Probability Distributions > Kumaraswamy distribution What is the Kumaraswamy distribution? The Kumaraswamy distribution was originally proposed by Indian hydrologist Poondi Kumaraswamy in 1980 [1] for variables with lower and upper bounds with a zero-inflation. It is a two-variable family of distributions that is bounded at one and zero. In other words, probabilities outside of the range of … Read more

Probability Distributions > J Shaped Distribution A J shaped distribution is a probability distribution where the majority of the observations fall at one end of the distribution while very few are located in the middle, giving the distribution the rough shape of the letter J laid on its side. This distribution pattern indicates that the … Read more

Probability Distributions > Folded Normal Distribution Contents: Folded Normal Distribution Half Normal Distribution What is a Folded Normal Distribution? The folded normal distribution is defined as the absolute value of the normal distribution [1]. It can be used to describe what happens when only the magnitude of a random variable is recorded, but not its sign. … Read more

Probability distributions > Loglinear model / distribution What is a loglinear model / distribution? The log-linear distribution models the log-probability of outcomes as a linear function of features. It is not commonly used in statistics. However, log-linear distributions are widely used in machine learning domains such as natural language processing, softmax regression, and text mining. … Read more