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Math and Statistical Distributions 707
Probability distributions
Distribution Geometric
HyperExponential Hypergeometric
Inverse Gaussian
Inverse Weibull Johnson SB
Johnson SU
Laplace Logarithmic
Logistic
Log-Logistic LogNormal
Negative Binomial
Definition
Outputs the number of failures before the first success in a sequence of inde- pendent Bernoulli trials with the probability of success on each trial. Typi- cally used for the number of items inspected before encountering the first defective item, the number of items in a batch of random size, or the number of items demanded from an inventory.
Usually used in telephone traffic and queueing theory.
Describes the number of defects, x, in a sample of size s from a population of size N which has m total defects. It is used to describe sampling from a population where an estimate of the total number of defects is desired. It has also been used to estimate the total population of species from a tagged sub- set.
Originally used to model Brownian motion and diffusion processes with boundary conditions. It has also been used to model the distribution of parti- cle size in aggregates, reliability and lifetimes, and repair time.
Describes several failure processes as a distribution of lifetime. It can also be used to fit data with abnormal large outliers on the positive side of the peak.
Used in quality control to describe non-normal processes, which can then be transformed to the Normal distribution for use with standard tests. It is a continuous distribution that has both upper and lower finite bounds.
Used in quality control to describe non-normal processes, which can then be transformed to the Normal distribution for use with standard tests. It is an unbounded continuous distribution.
Used in error analysis and to describe the difference of two independent, and equally distributed, exponentials.
Describes the diversity of a sample, that is, how many of a given type of thing are contained in a sample of things. For instance, this distribution has been used to describe the number of individuals of a given species in a sam- pling of mosquitoes, or the number of parts of a given type in a sampling of inventory.
Most often used a growth model: for populations, for weight gain, for busi- ness failure, etc. Can also be used to test for the suitability of such a model, with transformation to get back to the minimum and maximum values for the Logistic function. Occasionally used in place of the Normal function where exceptional cases play a larger role.
For Shape = 1, it resembles the Exponential distribution. For Shape < 1, it tends to infinity at Location, and decreases with increasing X. For Shape > 1, it is zero at Location, and then peaks and decreases.
Often used to represent the time to perform an activity (especially when there are multiple sub-activities), the time between failures, or the duration of manual activities. This distribution is widely used in business for security or property valuation, such as the rate of return on stock or real estate returns.
Number of failures before Sth success. P specifies the probability of success.
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