The maximum likelihood estimates MLEs are the parameter estimates that maximize the likelihood function for fixed values of x. The maximum likelihood estimators of a and b for the Weibull distribution are the solution of the simultaneous equations. To fit the Weibull distribution to data and find parameter estimates, use wblfit , fitdist , or mle.
Unlike wblfit and mle , which return parameter estimates, fitdist returns the fitted probability distribution object WeibullDistribution. The object properties a and b store the parameter estimates. For an example, see Compute Weibull Distribution pdf. The result p is the probability that a single observation from a Weibull distribution with parameters a and b falls in the interval [0 x ].
For an example, see Compute Weibull Distribution cdf. The result x is the value where an observation from a Weibull distribution with parameters a and b falls in the range [0 x ] with probability p.
The hazard function instantaneous failure rate is the ratio of the pdf and the complement of the cdf. Simulate the tensile strength data of a thin filament using the Weibull distribution with the scale parameter value 0. The estimated scale parameter is 0. The estimated shape parameter is 1. Compute and plot the pdf of the Weibull distribution for various values of the scale A and shape B parameters. Compute and plot the cdf of the Weibull distribution for various values of the scale A and shape B parameters.
The exponential distribution has a constant hazard function, which is not generally the case for the Weibull distribution. In this example, the Weibull hazard rate increases with age a reasonable assumption. Rayleigh Distribution — The Rayleigh distribution is a one-parameter continuous distribution that has parameter b scale. Statistical Analysis of Reliability Data. Non-Uniform Random Variate Generation.
Statistical Distributions. New York: J. Wiley, Statistical Models and Methods for Lifetime Data. Wiley Series in Probability and Statistics.
Hoboken, N. J: Wiley-Interscience, Statistical Methods for Reliability Data. Applied Probability and Statistics Section. New York: Wiley, WeibullDistribution wblcdf wblpdf wblinv wbllike wblstat wblfit wblrnd wblplot mle. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. The three-parameter Weibull distribution adds a location parameter that is zero in the two-parameter case.
For more details, see Three-Parameter Weibull Distribution. The likelihood function is the probability density function pdf viewed as a function of the parameters. The maximum likelihood estimates MLEs are the parameter estimates that maximize the likelihood function for fixed values of x. The maximum likelihood estimators of a and b for the Weibull distribution are the solution of the simultaneous equations. To fit the Weibull distribution to data and find parameter estimates, use wblfit , fitdist , or mle.
Unlike wblfit and mle , which return parameter estimates, fitdist returns the fitted probability distribution object WeibullDistribution. The object properties a and b store the parameter estimates. For an example, see Compute Weibull Distribution pdf. The result p is the probability that a single observation from a Weibull distribution with parameters a and b falls in the interval [0 x ]. For an example, see Compute Weibull Distribution cdf. The result x is the value where an observation from a Weibull distribution with parameters a and b falls in the range [0 x ] with probability p.
The hazard function instantaneous failure rate is the ratio of the pdf and the complement of the cdf. Simulate the tensile strength data of a thin filament using the Weibull distribution with the scale parameter value 0.
The estimated scale parameter is 0. The estimated shape parameter is 1. Compute the density of the observed value 3 in the Weibull distributions with scale parameter 2 and shape parameters 1 through 5. Compute the density of sample observations in the exponential distributions with means 1 through 5 using expcdf.
Compute the density of the same sample observations using wblpdf where the scale parameter is equal to mu and the shape parameter is 1. Values at which to evaluate the pdf, specified as a nonnegative scalar value or an array of nonnegative scalar values. To evaluate the pdf at multiple values, specify x using an array.
To evaluate the pdfs of multiple distributions, specify a and b using arrays. If one or more of the input arguments x , a , and b are arrays, then the array sizes must be the same. In this case, wblpdf expands each scalar input into a constant array of the same size as the array inputs. Each element in y is the pdf value of the distribution specified by the corresponding elements in a and b , evaluated at the corresponding element in x. Example: [3 4 7 9].
Data Types: single double.
0コメント