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In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The finiteness of the weakest-link chain model causes major deviations from the Weibull distribution. As the structure size, measured by , increases, the grafting point of the Weibullian left part moves to the right until, at about =, the entire distribution becomes Weibullian. The mean strength can be computed from this distribution and, as it ...
In the four survival function graphs shown above, the shape of the survival function is defined by a particular probability distribution: survival function 1 is defined by an exponential distribution, 2 is defined by a Weibull distribution, 3 is defined by a log-logistic distribution, and 4 is defined by another Weibull distribution.
They showed that the exponentiated Weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates. The exponentiated exponential distribution proposed by Gupta and Kundu (1999, 2001) is a special case of the exponentiated Weibull family. Later, the moments of the EW distribution were derived by Choudhury (2005).
CDF of a bimodal Weibull distribution with Weibull Moduli of 4 and 10 and characteristic strengths of 40 and 120 MPa Examples of a bimodal Weibull PDF and CDF are plotted in the figures of this article with values of the characteristic strength being 40 and 120 MPa, the Weibull moduli being 4 and 10, and the value of Φ is 0.5, corresponding to ...
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function ( ) = > . where α > 0 is a shape parameter.
The q-Weibull is equivalent to the Weibull distribution when q = 1 and equivalent to the q-exponential when = The q -Weibull is a generalization of the Weibull, as it extends this distribution to the cases of finite support ( q < 1) and to include heavy-tailed distributions ( q ≥ 1 + κ κ + 1 ) {\displaystyle (q\geq 1+{\frac {\kappa }{\kappa ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...