# Category: Uncategorized

• ## Arcsine Distribution

Probability Distribution List > The arcsine distribution is a probability distribution with a cumulative distribution function (CDF) involving the arcsine. It is so-named because “arcsin x” is the arc with a sine of x – where sine is a trigonometric function that gives one of three possible ratios of the lengths of a triangle’s sides. The distribution is […]

• ## Marshall-Olkin Bivariate Distribution.

< Probability Distribution List The Marshall–Olkin bivariate distribution, introduced by Albert W. Marshall and Ingram Olkin , is a family of continuous multivariate probability distributions that is an extension of the bivariate family of distributions with an extra shape parameter α. It is defined by the proper survival function Where (X, Y) is a random vector with joint […]

• ## Discrete Weibull Distribution

< Probability distributions The discrete Weibull distribution is the discrete variant of the Weibull distribution. It is used to model lifetime data expressed by discrete random variables. For example, it can be used to model equipment that operates in cycles, devices with on/off switches, or equipment with to-and-from motion. Types of Discrete Weibull Distribution Three […]

• ## Wrapped Normal Distribution

List of probability distributions > The wrapped normal distribution (or wrapped up normal distribution) occurs via Brownian motion on a circle.  It is the circular analog of a normal distribution, achieved by wrapping the probability density function (PDF) of a real-valued, linear random variable to the circumference of a unit circle an infinite number of […]

• ## Linear Exponential Distribution

Probability Distributions List > The linear exponential (LE) distribution is an extension of the exponential distribution. It is often used in actuarial science and survival analysis, where it is sometimes called the linear failure rate distribution. The LE describes survival patterns with constant initial hazard rates. The “linear” part of the distribution is the hazard rate, […]

• ## Eulerian Distribution

< Back to Probability Distribution List The term “Eulerian distribution” may refer to: A distribution used in permutation statistics to count descents, or A Type III (p/q, p) distribution. Eulerian Distribution in Permutation Statistics In permutation statistics, the Eulerian distribution is the classical name for the distribution of the descent statistics. A descent in a […]

• ## Bipolar Distribution

< Back to Probability Distribution List A bipolar distribution is a specific type of bimodal distribution that has two distinct peaks offering contradictory information. In some cases, the term may also refer to the Watson bipolar distribution. Bimodal vs. Bipolar Distribution A bimodal distribution is a distribution with two distinct peaks or modes. The modes […]

• ## Variance Ratio Distribution

< Back to Probability Distribution List The “variance ratio distribution” refers to the distribution of the ratio of variances of two samples drawn from a normal bivariate correlated population. Today, we call this the bivariate normal distribution. The Fisher-Snedicor F Distribution is sometimes called the “Variance Ratio” distribution because it is the distribution of the […]

• ## Poisson Distribution

< Back to Probability Distribution List A Poisson distribution, named for French mathematician Siméon Denis Poisson, predicts the occurrence of certain events in an interval (e.g., time, distance, volume) if you know how often the event has occurred. Most applications of the distribution are used to model the number of events happening in a fixed interval […]

• ## Kullbach Distribution

< Back to Probability Distributions I love a good mystery. I found a reference to the Kullbach distribution while researching unusual probability distributions. Of course, the first thing I did was to perform a Google search for “Kullbach distribution”. I got exactly one result from Haight  So, what exactly is this mysterious distribution? A […]