Parametric Estimation Methods For The Generalized Modified Weibull Distribution

For more than half of a century Weibull distribution has attracted the attention of many statisticians working on theories and methods as well as various fields of applied statistics, and a great deal of research work are made. Togethering with the normal, exponential and t-distributions, Weibull distribution has been a most popular model in modern statistics and is widely used to fit data from various fields such as life data, weather data and economic data. But with the developed technology and richer data types, Weibull distribution does not provide a reasonable parametric model for phenomena with non-monotone failure rates such as the bathtub-shaped and the unimodal failure. To solve this kind of problem, a new distribution has been presented, which is called the generalized modified Weibull (GMW) distribution with four parameters. This new distribution can overcome some limits of Weibull distribution and can flexibly accommodate all the forms of the hazard rate function including monotone and non-monotone cases. In the literature, some basic statistics (e.g., moment, order statistics) of this distribution have been given and maximum likelihood estimation for its parameters is only utilized on censored data. But we know that there are many parametric estimation methods which can directly influence estimation results. In order to use widely this distribution in practice, we investigate several estimation methods for parameters and make statistical analysis and comparison for them.Our main research works are as follows:1. As for the case that only maximum likelihoods estimation is used on censored data, we use maximum likelihood, method of moments, quantile-based estimation, least-squares and weighted least-squares methods estimate parameters of GMW distribution on all sample again and give their theoretical analysis and derivations.2. In order to tradeoff between advantages and disadvantages of a variety of algorithms on different sample sizes and different parametric values, we perform extensive simulation experiments and give corresponding statistical analysis and conclusions in terms of mean-squared errors (MSE) and biases.