|
& x\geq0\\ 0 & x<0\end| cdf =| mean =| median =| mode =| arg mode = if | variance =| skewness =| kurtosis =(see text)| entropy =| mgf = | char = }} In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1951, although it was first identified by and first applied by to describe a particle size distribution. ==Definition== The probability density function of a Weibull random variable is: : where ''k'' > 0 is the ''shape parameter'' and λ > 0 is the ''scale parameter'' of the distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other probability distributions; in particular, it interpolates between the exponential distribution (''k'' = 1) and the Rayleigh distribution (''k'' = 2 and 〔http://www.mathworks.com.au/help/stats/rayleigh-distribution.html〕). If the quantity ''X'' is a "time-to-failure", the Weibull distribution gives a distribution for which the failure rate is proportional to a power of time. The ''shape'' parameter, ''k'', is that power plus one, and so this parameter can be interpreted directly as follows: * A value of ''k'' < 1 indicates that the failure rate decreases over time. This happens if there is significant "infant mortality", or defective items failing early and the failure rate decreasing over time as the defective items are weeded out of the population. * A value of ''k'' = 1 indicates that the failure rate is constant over time. This might suggest random external events are causing mortality, or failure. * A value of ''k'' > 1 indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more likely to fail as time goes on. In the field of materials science, the shape parameter ''k'' of a distribution of strengths is known as the Weibull modulus. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Weibull distribution」の詳細全文を読む スポンサード リンク
|