matlab帕累托分布函数,matlab 进行广义的帕累托参数估计

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parmhat = gpfit(X) 产生pareto随机数

参数估计，

[parmhat,parmci] = gpfit(X)

参数估计，有alpha

[parmhat,parmci] = gpfit(X,alpha)

GPFIT Parameter estimates and confidence intervals for generalized Pareto data.

PARMHAT = GPFIT(X) returns maximum likelihood estimates of the parameters

of the two-parameter generalized Pareto (GP) distribution given the data

in X.  PARMHAT(1) is the tail index (shape) parameter, K and PARMHAT(2) is

the scale parameter, SIGMA.  GPFIT does not fit a threshold (location)

parameter.

[PARMHAT,PARMCI] = GPFIT(X) returns 95% confidence intervals for the

parameter estimates.

[PARMHAT,PARMCI] = GPFIT(X,ALPHA) returns 100(1-ALPHA) percent confidence

intervals for the parameter estimates.

[...] = GPFIT(X,ALPHA,OPTIONS) specifies control parameters for the

iterative algorithm used to compute ML estimates. This argument can be

created by a call to STATSET.  See STATSET('gpfit') for parameter names

and default values.

Pass in [] for ALPHA to use the default values.

Other functions for the generalized Pareto, such as GPCDF, allow a

threshold parameter THETA.  However, GPFIT does not estimate THETA, and it

must be assumed known, and subtracted from X before calling GPFIT.

When K = 0 and THETA = 0, the GP is equivalent to the exponential

distribution.  When K > 0 and THETA = SIGMA, the GP is equivalent to the

Pareto distribution. The mean of the GP is not finite when K >= 1, and the

variance is not finite when K >= 1/2.  When K >= 0, the GP has positive

density for X>THETA, or, when K < 0, for 0 <= (X-THETA)/SIGMA <= -1/K.