Examples of "weibull_distribution"
In probability theory and statistics, the discrete Weibull distribution is the discrete variant of the Weibull distribution. It was first described by Nakagawa and Osaki in 1975.
The cumulative distribution function for the Weibull distribution is
This rule does not hold for the unimodal Weibull distribution.
The cumulative distribution function for the exponentiated Weibull distribution is
In statistics, the q-Weibull distribution is a probability distribution that generalizes the Weibull distribution and the Lomax distribution (Pareto Type II). It is one example of a Tsallis distribution.
have been known to use the name "stretched exponential" to refer to the Weibull distribution.
The quantile (inverse cumulative distribution) function for the Weibull distribution is
and the density function of the weibull distribution is given as:
Bernoulli distribution, Geometric distribution, Exponential distribution, Extreme value distribution, Pareto distribution, Rayleigh distribution, Weibull distribution.
If the probability distribution of the strength, "X", is a Weibull distribution with its density given by
The q-Weibull is equivalent to the Weibull distribution when "q" = 1 and equivalent to the q-exponential when formula_12
Normal distribution, Gamma distribution, Cauchy distribution, Exponential distribution, Erlang distribution, Weibull distribution, Logistic distribution, Error distribution, Power distribution, Rayleigh distribution.
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.
The Weibull modulus is a dimensionless parameter of the Weibull distribution which is used to describe variability in measured material strength of brittle materials.
The Fréchet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function
In 1951 he presented his most famous paper to the American Society of Mechanical Engineers (ASME) on the Weibull distribution, using seven case studies.
If formula_10 then the generalized gamma distribution becomes the Weibull distribution. Alternatively, if formula_11 the generalised gamma becomes the gamma distribution.
Remark II: The ordinary Weibull distribution arises in reliability applications and is obtained from the distribution here by using the variable formula_46, which gives a strictly positive support - in contrast to the use in the extreme value theory here. This arises because the Weibull distribution is used in cases that deal with the minimum rather than the maximum. The distribution here has an addition parameter compared to the usual form of the Weibull distribution and, in addition, is reversed so that the distribution has an upper bound rather than a lower bound. Importantly, in applications of the GEV, the upper bound is unknown and so must be estimated while when applying the Weibull distribution the lower bound is known to be zero.
The family of distributions accommodates unimodal, bathtub shaped* and monotone failure rates. A similar distribution was introduced in 1984 by Zacks, called a Weibull-exponential distribution (Zacks 1984). Crevecoeur introduced it in assessing the reliability of ageing mechanical devices and showed that it accommodates bathtub shaped failure rates (1993, 1994). Mudholkar, Srivastava, and Kollia (1996) applied the generalized Weibull distribution to model survival data. They showed that the distribution has increasing, decreasing, bathtub, and unimodal hazard functions. Mudholkar, Srivastava, and Freimer (1995), Mudholkar and Hutson (1996) and Nassar and Eissa (2003) studied various properties of the exponentiated Weibull distribution. Mudholkar et al. (1995) applied the exponentiated Weibull distribution to model failure data. Mudholkar and Hutson (1996) applied the exponentiated Weibull distribution to extreme value data. 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). Also, M. Pal, M.M. Ali, J. Woo (2006) studied the EW distribution and compared it with the two-parameter Weibull and gamma distributions with respect to failure rate.
The continuous Weibull distribution has a close relationship with the Gumbel distribution which is easy to see when log-transforming the variable. A similar transformation can be made on the discrete-weibull.