Journal of Data Science

ABSTRACT：A new distribution called the exponentiated Burr XII Weibull(EBW) distributions is proposed and presented. This distribution contains several new and known distributions such as exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential, exponentiated Lomax Weibull, exponentiated Lomax Rayleigh, exponentiated Lomax Exponential, Lomax Weibull, Lomax Rayleigh Lomax exponential, Weibull, Rayleigh, exponential and log-logistic distributions as special cases. A comprehensive investigation of the properties of this generalized distribution including series expansion of probability density function and cumulative distribution function, hazard and reverse hazard functions, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R´enyi entropy and distribution of order statistics are presented. Parameters of the model are estimated using maximum likelihood estimation technique and real data sets are used to illustrate the usefulness and applicability of the new generalized distribution compared with other distributions.

Minimum Hellinger distance estimation (MHDE) for parametric model is obtained by minimizing the Hellinger distance between an assumed parametric model and a nonparametric estimation of the model. MHDE receives increasing attention for its efficiency and robustness. Recently, it has been extended from parametric models to semiparametric models. This manuscript considers a two-sample semiparametric location-shifted model where two independent samples are generated from two identical symmetric distributions with different location parameters. We propose to use profiling technique in order to utilize the information from both samples to estimate unknown symmetric function. With the profiled estimation of the function, we propose a minimum profile Hellinger distance estimation (MPHDE) for the two unknown location parameters. This MPHDE is similar to but dif- ferent from the one introduced in Wu and Karunamuni (2015), and thus the results presented in this work is not a trivial application of their method. The difference is due to the two-sample nature of the model and thus we use different approaches to study its asymptotic properties such as consistency and asymptotic normality. The efficiency and robustness properties of the proposed MPHDE are evaluated empirically though simulation studies. A real data from a breast cancer study is analyzed to illustrate the use of the proposed method.

In this paper, we define and study a four-parameter model called the transmuted Burr XII distribution. We obtain some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics, probability weighted moments and entropies. We formulate and develop a log-linear model using the new distribution so-called the log-transmuted Burr XII distribution for modeling data with a unimodal failure rate function, as an alternative to the log-McDonald Burr XII, log-beta Burr XII, log-Kumaraswamy Burr XII, log-Burr XII and logistic regression models. The flexibility of the proposed models is illustrated by means of three applications to real data sets.

Abstract:In medical literature, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In the recent years, the Poisson regression model has been widely used particularly. However, it is also recognized that the count or frequency data in medical practice often display over-dispersion, i.e., a situation where the variance of the response variable exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standart errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This article suggests the Negative Binomial (NB) and Conway-Maxwell-Poisson (COM-Poisson) regression models as an alternatives for handling overdispersion. All mentioned regression models are applied to simulation data and dataset of hospitalization number of people with schizophrenia, the results are compared.

Abstract: The paper deals with the introduction of new generalized model i.e., Rayleigh Lomax distribution. In this manuscript, a comprehensive description of the various structural properties of the new proposed model including explicit expressions for moments, quantile function, generating functions and Renyi entropy have been given. The parameters of the newly developed distribution have been estimated using the technique of maximum likelihood estimation. Also, the generalized model has been compared with different models for illustration and best fit.

Abstract:A new generalized two-parameter Lindley distribution which offers more flexibility in modeling lifetime data is proposed and some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, mean residual life function, moment generating function, quantile function, moments, Renyi entropy and stochastic ordering are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimators of the parameters. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit attained by some existing lifetime distributions.

Abstract:This paper has been proposed to estimate the parameters of Markov based logistic model by Bayesian approach for analyzing longitudinal binary data. In Bayesian estimation selection of appropriate loss function and prior density are most important ingredient. Symmetric and asymmetric loss functions have been used for estimating parameters of two state Markov model and better performance has been observed by Bayesian estimate under squared error loss function.

It is well known that under certain regularity conditions the boot- strap sampling distributions of common statistics are consistent with their true sampling distributions. However, the consistency results rely heavily on the underlying regularity conditions and in fact, a failure to satisfy some of these may lead us to a serious departure from consistency. Consequently, the ‘sufficient bootstrap’ method (which only uses distinct units in a bootstrap sample in order to reduce the computational burden for larger sample sizes) based sampling distributions will also be inconsistent. In this paper, we combine the ideas of sufficient and m-out-of-n (m/n) bootstrap methods to regain consistency. We further propose the iterated version of this bootstrap method in non-regular cases and our simulation study reveals that similar or even better coverage accuracies than percentile bootstrap confidence inter- vals can be obtained through the proposed iterated sufficient m/n bootstrap with less computational time each case.

bstract: In this article we propose further extension of the generalized Marshall Olkin-G ( GMO - G ) family of distribution. The density and survival functions are expressed as infinite mixture of the GMO - G distribution. Asymptotes, Rényi entropy, order statistics, probability weighted moments, moment generating function, quantile function, median, random sample generation and parameter estimation are investigated. Selected distributions from the proposed family are compared with those from four sub models of the family as well as with some other recently proposed models by considering real life data fitting applications. In all cases the distributions from the proposed family out on top.

The power generalized Weibull distribution due to Bagdonovacius and Nikulin (2002) is an alternative,and always provides better fits than the exponentiated Weibull family for modeling lifetime data. In this paper, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence relations for the single, product and conditional moments of generalized order statistics from the power generalized Weibull distribution and then we use these results to compute the means and variances of order statistics and record values for samples of different sizes for various values of the shape and scale parameters.