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Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.
The probability density, cumulative distribution, and inverse cumulative distribution of any function of one or more independent or correlated normal variables can be computed with the numerical method of ray-tracing [41] (Matlab code). In the following sections we look at some special cases.
The function A(t | ν) is the integral of Student's probability density function, f(t) between -t and t, for t ≥ 0 . It thus gives the probability that a value of t less than that calculated from observed data would occur by chance.
The complementary cumulative distribution function (ccdf) or the tail distribution is defined as ... In short, the probability density function (pdf) of a ...
Unlike the more commonly used Weibull distribution, it can have a non-monotonic hazard function: when >, the hazard function is unimodal (when ≤ 1, the hazard decreases monotonically). The fact that the cumulative distribution function can be written in closed form is particularly useful for analysis of survival data with censoring . [ 9 ]
The uniform distribution is useful for sampling from arbitrary distributions. A general method is the inverse transform sampling method, which uses the cumulative distribution function (CDF) of the target random variable. This method is very useful in theoretical work.
libstable is a C implementation for the Stable distribution pdf, cdf, random number, quantile and fitting functions (along with a benchmark replication package and an R package). R Package 'stabledist' by Diethelm Wuertz, Martin Maechler and Rmetrics core team members. Computes stable density, probability, quantiles, and random numbers.