Abstract
The Weibull distribution has received much interest in reliability theory. The well-known maximum likelihood estimators (MLE) of this fam ily are not available in closed form expression. In this work, we propose a consistent and closed form estimator for shape parameter of three-parameter Weibull distribution. Apart from high degree of performance, the derived estimator is location and scale-invariant.
Highlights
The use of Weibull distribution to describe real phenomena has a long history
As the most efficient one which received a lot of attention in the literature, maximum likelihood estimators (MLE) of Weibull family is derived by solving the non-linear set of three equations given as follows: nn + log xi − μ n xi − μ α log xi − μ
The histogram is constructed from 500 points, with account taken of the fact that each point is obtained via the MLE or new estimator on the basis of a sample of size 100 generated from (1.1)
Summary
The use of Weibull distribution to describe real phenomena has a long history. This distribution was originally proposed by the Swedish physicist Waloddi Weibull. He used it for modeling the distribution of breaking strength of materials. Since it has received applications in many areas. The hazard rate function corresponding to (1.1) and (1.2) is α x − μ α−1. The Weibull distribution can allow for decreasing, constant and increasing hazard rates. This is one of the attractive properties that made the Weibull distribution so applicable. The most popular and the most efficient of these is the maximum likelihood estimation
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