BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate

A New Generalization of Power Garima Distribution with Applications in Blood Cancer and Relief Times

The present study deals with the weighted version of power Garima distribution and its various statistical properties have been obtained. For estimating its parameters, the technique of maximum likelihood estimation have been used and also observed its Fisher’s information matrix. Finally, the two real lifetime data sets from medical sciences have been used to discuss the superiority of new distribution

On Weighted Nwikpe Distribution: Properties and Applications

In this article, two-parameter continuous distribution is introduced. The proposed distribution is obtained by using a weight technique and is referred to as weighted Nwikpe distribution. This distribution is a generalization of baseline distribution that is Nwikpe distribution. Some structural properties of the distribution are derived. These are density function, distribution function, and reliability function, hazard rate function, moments, moment generating function, entropies, order statistics, Bonferroni and Lorenz curves. The method of maximum likelihood estimation has been established for investigating the parameters of the model. The behaviour of the parameters of the distribution is examined by a simulation study. Real data set is used to determine whether the weighted Nwikpe distribution is better than other well-known distributions in modeling data or not

The extended gamma distribution with regression model and applications

This paper introduces a new extension of the gamma distribution, named as a new extended gamma distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model