The New Kumaraswamy Kumaraswamy Weibull Distribution with Application

<p>             The Weibull distribution has been used over the past decades for modeling data in many fields so finding generalization of the Weibull distribution becomes very useful to fit more cases or get better fits than before. In this paper, the Kumaraswamy  Kumaraswamy Weibull (Kw Kw W) distribution is presented for the first time and we show that it is generalizes many important distribution. The probability density function (pdf), the cumulative distribution function (cdf), moments, quantiles, the median, the mode, the mean deviation, the entropy, order statistics, L-moments, extreme value and parameters estimation based on maximum likelihood are obtained for the Kumaraswamy Kumaraswamy Weibull distribution. A simulation study and a real data set is used to illustrate the potentiality and application of the new Kumaraswamy Kumaraswamy Weibull distribution.</p

The New Kumaraswamy Kumaraswamy Weibull Distribution with Application

             The Weibull distribution has been used over the past decades for modeling data in many fields so finding generalization of the Weibull distribution becomes very useful to fit more cases or get better fits than before. In this paper, the Kumaraswamy  Kumaraswamy Weibull (Kw Kw W) distribution is presented for the first time and we show that it is generalizes many important distribution. The probability density function (pdf), the cumulative distribution function (cdf), moments, quantiles, the median, the mode, the mean deviation, the entropy, order statistics, L-moments, extreme value and parameters estimation based on maximum likelihood are obtained for the Kumaraswamy Kumaraswamy Weibull distribution. A simulation study and a real data set is used to illustrate the potentiality and application of the new Kumaraswamy Kumaraswamy Weibull distribution

Odds Generalized Exponential-Inverse Weibull Distribution: Properties & Estimation

Providing extended and generalized distribution is usually precious for many statisticians. A new distribution, called odds generalized exponential-inverse Weibull distribution (OGE-IW) is suggested for modeling lifetime data. Some structural properties of the new distribution are obtained. Three different estimation procedures, namely; maximum likelihood, percentiles and least squares, have been used to estimate the model parameters of subject distribution. The consistency of the parameters of the OGE-IW distribution is demonstrated through a simulation study. A real data application is presented to illustrate the importance of the new distribution compared with some known distributions

Estimation of Information Measures for Power-Function Distribution in Presence of Outliers and Their Applications

Entropy measurement plays an important role in the field of information theory. Furthermore, the estimation of entropy is an important issue in statistics and machine learning. This study estimated the Rényi and q-entropies of a power-function distribution in the presence of s outliers using classical and Bayesian procedures. In the classical method, the maximum likelihood estimators of the entropies were obtained and their performance was assessed through a numerical study. In the Bayesian method, the Bayesian estimators of the entropies under uniform and gamma priors were acquired based on different loss functions. The Bayesian estimators were computed empirically using a Monte Carlo simulation based on the Gibbs sampling algorithm. The simulated datasets were analyzed to investigate the accuracy of the estimates. The study results showed that the precision of the maximum likelihood and Bayesian estimates of both entropies improved with increasing the sample size and the number of outliers. The absolute biases and the mean squared errors of the estimates in the presence of outliers exceeded those of the corresponding estimates in the homogenous case (no-outliers). Furthermore, the Bayesian estimates of the Rényi and q-entropies under the squared error loss function were preferable to the other Bayesian estimates in a majority of the cases. Finally, analysis results of real data examples were consistent with those of the simulated data

On Discriminating between Gamma and Log-logistic Distributions in Case of Progressive Type II Censoring

Gamma and log-logistic distributions are two popular distributions for analyzing lifetime data. In this paper, the problem of discriminating between these two distribution functions is considered in case of progressive type II censoring. The ratio of the maximized likelihood test (RML) is used to discriminate between them. Some simulation experiments were performed to see how the probability of correct selection (PCS) under each model work for small sample sizes. Real data life is analyzed to see how the proposed method works in practice. As a special case of progressive type II censoring, the problem of discriminating between gamma and log-logistic in case of complete samples is considered. The RML and the ratio of Minimized Kullback-Leibler Divergence (RMKLD) tests are used to discriminate between them. The asymptotic results are used to estimate the PCS which is used to calculate the minimum sample size required for discriminating between two distributions. Two real life data are analyzed