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cdf
Cumulative distribution functions
Syntax
Y = cdf('name',X,A)
Y = cdf('name',X,A,B)
Y = cdf('name',X,A,B,C)
Description
Y = cdf('name',X,A) computes the cumulative distribution function for the one-parameter family of distributions specified by name. A contains parameter values for the distribution. The cumulative distribution function is evaluated at the values in X and its values are returned in Y.
If X and A are arrays, they must be the same size. If X is a scalar, it is expanded to a constant matrix the same size as A. If A is a scalar, it is expanded to a constant matrix the same size as X.
Y is the common size of X and A after any necessary scalar expansion.
Y = cdf('name',X,A,B) computes the cumulative distribution function for two-parameter families of distributions, where parameter values are given in A and B.
If X, A, and B are arrays, they must be the same size. If X is a scalar, it is expanded to a constant matrix the same size as A and B. If either A or B are scalars, they are expanded to constant matrices the same size as X.
Y is the common size of X, A, and B after any necessary scalar expansion.
Y = cdf('name',X,A,B,C) computes the cumulative distribution function for three-parameter families of distributions, where parameter values are given in A, B, and C.
If X, A, B, and C are arrays, they must be the same size. If X is a scalar, it is expanded to a constant matrix the same size as A, B, and C. If any of A, B or C are scalars, they are expanded to constant matrices the same size as X.
Y is the common size of X, A, B, and C after any necessary scalar expansion.
Acceptable strings for name (specified in single quotes) are:
| name | Distribution | Input Parameter A | Input Parameter B | Input Parameter C |
|---|---|---|---|---|
| 'beta' or 'Beta' | Beta Distribution | a | b | — |
| 'bino' or 'Binomial' | Binomial Distribution | n: number of trials | p: probability of success for each trial | — |
| 'birnbaumsaunders' | Birnbaum-Saunders Distribution | β | γ | — |
| 'burr' or 'Burr' | Burr Type XII Distribution | α: scale parameter | c: shape parameter | k: shape parameter |
| 'chi2' or 'Chisquare' | Chi-Square Distribution | ν: degrees of freedom | — | — |
| 'exp' or 'Exponential' | Exponential Distribution | μ: mean | — | — |
| 'ev' or 'Extreme Value' | Extreme Value Distribution | μ: location parameter | σ: scale parameter | — |
| 'f' or 'F' | F Distribution | ν1: numerator degrees of freedom | ν2: denominator degrees of freedom | — |
| 'gam' or 'Gamma' | Gamma Distribution | a: shape parameter | b: scale parameter | — |
| 'gev' or 'Generalized Extreme Value' | Generalized Extreme Value Distribution | k: shape parameter | σ: scale parameter | μ: location parameter |
| 'gp' or 'Generalized Pareto' | Generalized Pareto Distribution | k: tail index (shape) parameter | σ: scale parameter | μ: threshold (location) parameter |
| 'geo' or 'Geometric' | Geometric Distribution | p: probability parameter | — | — |
| 'hyge' or 'Hypergeometric' | Hypergeometric Distribution | M: size of the population | K: number of items with the desired characteristic in the population | n: number of samples drawn |
| 'inversegaussian' | Inverse Gaussian Distribution | μ | λ | — |
| 'logistic' | Logistic Distribution | μ | σ | — |
| 'loglogistic' | Loglogistic Distribution | μ | σ | — |
| 'logn' or 'Lognormal' | Lognormal Distribution | μ | σ | — |
| 'nakagami' | Nakagami Distribution | μ | ω | — |
| 'nbin' or 'Negative Binomial' | Negative Binomial Distribution | r: number of successes | p: probability of success in a single trial | — |
| 'ncf' or 'Noncentral F' | Noncentral F Distribution | ν1: numerator degrees of freedom | ν2: denominator degrees of freedom | δ: noncentrality parameter |
| 'nct' or 'Noncentral t' | Noncentral t Distribution | ν: degrees of freedom | δ: noncentrality parameter | — |
| 'ncx2' or 'Noncentral Chi-square' | Noncentral Chi-Square Distribution | ν: degrees of freedom | δ: noncentrality parameter | — |
| 'norm' or 'Normal' | Normal Distribution | μ: mean | σ: standard deviation | — |
| 'poiss' or 'Poisson' | Poisson Distribution | λ: mean | — | — |
| 'rayl' or 'Rayleigh' | Rayleigh Distribution | b: scale parameter | — | — |
| 'rician' | Rician Distribution | s: noncentrality parameter | σ: scale parameter | — |
| 't' or 'T' | Student's t Distribution | ν: degrees of freedom | — | — |
| 'tlocationscale' | t Location-Scale Distribution | μ: location parameter | σ: scale parameter | ν: shape parameter |
| 'unif' or 'Uniform' | Uniform Distribution (Continuous) | a: lower endpoint (minimum) | b: upper endpoint (maximum) | — |
| 'unid' or 'Discrete Uniform' | Uniform Distribution (Discrete) | N: maximum observable value | — | — |
| 'wbl' or 'Weibull' | Weibull Distribution | a: scale parameter | b: shape parameter | — |
Examples
Compute the cdf of the normal distribution with mean 0 and standard deviation 1 at inputs –2, –1, 0, 1, 2:
p1 = cdf('Normal',-2:2,0,1)
p1 =
0.0228 0.1587 0.5000 0.8413 0.9772
The order of the parameters is the same as for normcdf.
Compute the cdfs of Poisson distributions with rate parameters 0, 1, ..., 4 at inputs 1, 2, ..., 5, respectively:
p2 = cdf('Poisson',0:4,1:5)
p2 =
0.3679 0.4060 0.4232 0.4335 0.4405The order of the parameters is the same as for poisscdf.