• ## The Reproductive Property of Distributions

< Probability and Statistics Definitions In statistics, the reproductive property is the result that if two or more independent random variables having a certain distribution are added, the resulting random variable has distribution of the same type as that of the summands. This is an important property to be aware of when working with distributions. […]

• ## Array Distribution

< Probability Distributions List The array distribution refers to the conditional distribution of independent random variables X1 (given X2, … , Xn). As such, it is often used as a synonym for a conditional distribution (for example, Kotz et al. , Giri & Banerjee , Wadworth & Bryan ). The Encyclopedia of Statistical Sciences  […]

• ## Alpha distribution

< Probability Distributions List The alpha distribution has been used for tool wear problems and may be used in modeling lifetimes under an accelerated test condition, even though the mean does not exist. Johnson et al.  defines the probability density function (PDF) as: Where Φ is the standard normal distribution. There is a similarity between […]

• ## Birnbaum-Saunders distribution

< Probability Distributions List The Birnbaum-Saunders distribution represents the distribution of lifetimes for components under certain wear conditions. This unimodal distribution was originally formulated to model failures due to cracks, it is an example of a fatigue life distribution.The Probability Density Function (PDF) for the Birnbaum-Saunders distribution is : Where α is the shape parameter and β is […]

• ## Weibull Distribution

< List of probability distributions Weibull Distribution Weibull-Gnedenko Weibull-Rician Fréchet distribution (inverse Weibull) See also: Discrete Weibull distribution Weibull Distribution The Weibull distribution is a continuous probability distribution for assessing product reliability, analyzing life data and modeling failure times. It is an example of an extreme value distribution (EVD) and is sometimes called EVD Type III. […]

• ## Uniform Distribution.

< List of probability distributions A uniform distribution U(a, b), also called a rectangular distribution, is defined by two parameters: minimum, a. maximum, b. The area under the curve of the uniform distribution is always equal to 1. In the above graph, the area is:A = l x h = 3 * 0.333… = 1. Continuous and Discrete Uniform […]

• ## Benford Distribution

< Probability distribution list 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 follow a uniform distribution as […]

• ## 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 distribution. In quantum mechanics, the delta distribution has an entirely different meaning: it is the functional δ(Φ) that associates every test function Φ(x) a […]

• ## 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 […]