Category: Uncategorized

  • Gompertz-Rayleigh distribution

    < List of probability distributions The Gompertz-Rayleigh distribution is an extension of the Rayleigh distribution that allows for better modeling of highly-skewed datasets compared to compound distributions [1]. A similarly named but unrelated distribution is a generalized Gompertz-Rayleigh distribution, proposed by Bradley [2] as a potential survival distribution for modeling risk. Many other generalized forms […]

  • Unimodal Distribution

    < List of probability distributions A unimodal distribution is any distribution with a single peak, cluster, or high point (i.e., global maximum). It comes from the Latin word uni– (“one”) and Middle French modal (“measure”). More specifically, the probability density function (PDF), histogram, or other graph of the distribution has one distinct peak. For example, the […]

  • Delta Distribution

    < List of probability distributions What is a delta distribution? The term delta distribution may refer to either the zero-modified lognormal distribution developed by Aitchison and Brown or the Dirac delta function. Zero-modified lognormal distribution The zero-modified lognormal (delta) distribution is a mixture distribution with a positive probability of a zero observation; positive observations (i.e., […]

  • Bell-shaped distribution

    < List of probability distributions 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 peak in the center (i.e., they are unimodal distributions) and are symmetric: if you draw a vertical line down the center of the […]

  • Zero-modified normal distribution

    < List of probability distributions A zero-modified normal distribution is a normal distribution modified to put extra probability mass at 0. In other words, it’s a kind of mixture distribution where part of the population comes from a normal distribution but the rest of the population is all zeros [1]. The probability density function of […]

  • Bates Distribution

    < List of Probability Distributions The Bates Distribution (or rectangular mean distribution) resembles a normal distribution although it can also resemble several other distributions depending on how many items are in the sample. Triangular distribution: n = 2. Uniform distribution: n = 1. Unimodal (normal) distribution: n > 2. More formally, it is the probability distribution of the […]

  • Modified Normal Distribution

    < Probability Distributions List The term modified normal distribution (or equinormal distribution) may refer to any number of distributions that are similar in appearance to a normal distribution (in other words, it’s simply a normal distribution modified in some way). For example, the t distribution is one example of a modified normal distribution [1]. The […]

  • 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 [1], 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 […]