威布尔分布在Matlab中的命令

Uniform (Continuous) Distribution
Quantile-Quantile Plots Empirical Cumulative Distribution Function (CDF)
Hidden Markov Model Functions New Functions for Extreme Value Distributions
Statistics Toolbox wblcdf
Weibull cumulative distribution function (cdf)
Syntax
P = wblbcdf(X, A, B)
[P, PLO, PUP] = wblcdf(X, A, B, PCOV, alpha)
Description
P = wblbcdf(X, A, B) computes the cdf of the Weibull distribution with scale parameter A and shape parameter B, at each of the values in X. X, A, and B can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array of the same size as the other inputs. The default values for A and B are both 1. The parameters A and B must be positive.
[P, PLO, PUP] = wblcdf(X, A, B, PCOV, alpha) returns confidence bounds for P when the input parameters A and B are estimates. PCOV is the 2-by-2 covariance matrix of the estimated parameters. alpha has a default value of 0.05, and specifies 100(1 - alpha)% confidence bounds. PLO and PUP are arrays of the same size as P containing the lower and upper confidence bounds.
The function wblcdf computes confidence bounds for P using a normal approximation to the distribution of the estimate
and then transforms those bounds to the scale of the output P. The computed bounds give approximately the desired confidence level when you estimate m u, sigma, and PCOV from large samples, but in smaller samples other methods of computing the confidence bounds might be more accurate.
The Weibull cdf is
Examples
What is the probability that a value from a Weibull distribution with parameters a = 0.15 and b =0.8 is less than 0.5?
probability = wblcdf(0.5, 0.15, 0.8)
probability =
0.9272
How sensitive is this result to small changes in the parameters?
[A, B] = meshgrid(0.1:0.05:0.2,0.2:0.05:0.3);
probability = wblcdf(0.5, A, B)
probability =
vartestn wblfit
wblcdf wblinv
Statistics Toolbox wblinv
Inverse of the Weibull cumulative distribution function
Syntax
X = wblinv(P, A, B)
[X, XLO, XUP] = wblinv(P, A, B, PCOV, alpha)
Description
X = wblinv(P, A, B) returns the inverse cumulative distribution function (cdf) for a Weibull distribution with scale parameter A and shape parameter B, evaluated at the values in P. P, A, and B can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array of the same size as the other inputs. The default values for A and B are both 1.
[X, XLO, XUP] = wblinv(P, A, B, PCOV, alpha) returns confidence bounds for X when the input parameters A and B are estimates. PCOV is a 2-by-2 matrix containing the covariance matrix of the estimated parameters. alpha has a default value of 0.05, and specifies 100(1 - a lpha)% confidence bounds. XLO and XUP are arrays of the same size as X containing the lower and upper confidence bounds.
The function wblinv computes confidence bounds for X using a normal approximation to the distribution of the estimate
where q is the P th quantile from a Weibull distribution with scale and shape parameters both equal to 1. The computed bounds give approximately the desired confidence level when you estimate mu, sigma, and PCOV from large samples, but in smaller samples other methods of computing the confidence bounds might be more accurate.
The inverse of the Weibull cdf is
Examples
The lifetimes (in hours) of a batch of light bulbs has a Weibull distribution with parameters a = 200 and b = 6. What is the median lifetime of the bulbs?
life = wblinv(0.5, 200, 6)
life =
188.1486
What is the 90th percentile?
life = wblinv(0.9, 200, 6)
life =
wblfit wbllike
wblinv wblpdf
wbllike wblplot
wblpdf wblrnd
wblplot wblstat
wblrnd wishrnd。