Probability Distributions Wikipedia: A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.
Types of supported distributions pdf — Probability density functions cdf — Cumulative distribution functions inv — Inverse cumulative distribution functions stat — Distribution statistics functions fit — Distribution fitting functions like — Negative log-likelihood functions rnd — Random number generators
Supported Distributions Bernoulli Distribution Beta Distribution Binomial Distribution Birnbaum-Saunders Distribution Chi-Square Distribution Copulas
Supported Distributions Lognormal Distribution Multinomial Distribution Multivariate Gaussian Distribution Multivariate Normal Distribution Multivariate t Distribution Nakagami Distribution Negative Binomial Distribution Noncentral Chi-Square Distribution Noncentral F Distribution Noncentral t Distribution Nonparametric Distributions
2. Non parametric estimation You can also describe a data distribution by estimating its density. The ksdensity function does this using a kernel smoothing method. A nonparametric density estimate of the data above, using the default kernel and bandwidth, is given by:
Cumulative Distribution Functions Parametric Estimation Nonparametric Estimation
Inverse Cumulative Distribution Functions Each function in this family represents a parametric family of distributions. Input arguments are arrays of cumulative probabilities between 0 and 1 followed by a list of parameter values specifying a particular member of the distribution family.
Inverse Cumulative Distribution Functions The expinv function can be used to compute inverses of exponential cumulative probabilities:
Distribution Statistics Functions Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family. Functions return the mean and variance of the distribution, as a function of the parameters.
Distribution Statistics Functions For example, the wblstat function can be used to visualize the mean of the Weibull distribution as a function of its two distribution parameters:
Distribution Fitting Functions Fitting Supported Distributions Fitting Piecewise Distributions
Negative Log-Likelihood Functions Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by an array of data. Functions return the negative log-likelihood of the parameters, given the data.
Random Number Generators Each RNG represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by the dimensions of an array. RNGs return random numbers from the specified distribution in an array of the specified dimensions.
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