Abstract
Maximum likelihood and proportion estimators of the parameters of the discrete Weibull type II distribution with type I censored data are discussed. A simulation study is performed to generate data from this distribution for suggested values of its parameters and to get the Maximum likelihood estimates of the parameters numerically. The method of proportions suggested by Khan et al. (1989) is also used to estimate the model's parameters. Numerical examples are used to perform a comparison study between the two method results according the values of the estimates and their corresponding mean squared errors.
Highlights
The method of proportions suggested by Khan et al (1989) is used to estimate the model's parameters
Discrete versions of some continuous distributions were suggested by some researchers using different discretizing methods
The estimates of the parameter α from DW(II) (1.8, 0.1) for different n and the corresponding MSEs are given in Table 4.1d which constitutes of seven columns, the first column contains the percentage % from n (80%, 90%, 95%, 98%, and 100%), the second column contains the termination time γ (γ = 4, 5, 6, 7, and 9), the third column contains r, the fourth column contains the maximum likelihood (ML) estimate of α, the fifth column contains the MSE of the ML estimate of α, the sixth column contains the proportion estimate of α, and the seventh column contains the MSE of the proportion estimate of α
Summary
Discrete versions of some continuous distributions were suggested by some researchers using different discretizing methods. These methods and distributions were very good reviewed by Chakraborty (2015) and extensively studied by Muiftah (2018). The maximum likelihood (ML) and proportion estimators of the parameters of the discrete Weibull type II [DW(II)] distribution with type I censored data are discussed. Methods used to estimate the distribution parameters are introduced. A simulation study is performed to generate data from the suggested distribution and to get the ML estimates of the parameters. Tables and graphs are used to illustrate the distribution and the results in a good manner.
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