Papers by Mohammed Shakhatreh
Electronic Journal of Applied Statistical Analysis, 2020
We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Bu... more We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes.
Mathematics, 2021
Continuous and discrete distributions are essential to model both continuous and discrete lifetim... more Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estim...
Mathematics, 2020
In this paper, we introduce a new family of continuous distributions that is called the modified ... more In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering ...
Pakistan Journal of Statistics and Operation Research, 2020
This paper addresses the estimation of the unknown parameters of the alphapower exponential distr... more This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.
International Journal of Environmental Research and Public Health, 2017
Injuries (unintentional and intentional) are the main cause of death and disability worldwide, in... more Injuries (unintentional and intentional) are the main cause of death and disability worldwide, including Jordan. The main purpose of this hospital-based retrospective study was to identify characteristics, causes, and risk factors of unintentional injuries and violence among all adult patients who approached the Accidents and Emergency department because of injury in Northern Jordan. Data were collected retrospectively from four major hospitals from January 2008 to January 2013. A total of 2425 Jordanian individuals who accessed and were treated by the four hospitals were included in this study. The findings show that the majority of patients who approached the Accidents and Emergency departments in the four hospitals were males (n = 2044, 87.16%) versus females (n = 301, 12.8%). Violence was the most common reason of injury (70.66%), followed by road traffic crashes (23.21%). The most common anatomical locations of reported injuries were the head (38.74%), followed by abdomen/pelvis and lower back, among males and females (9.93%). Violence had a high significant effect on the site of injuries. Patients who had been injured to the head because of a stab wound or fighting were substantially over-involved in head injuries, with injury rates 3.88 and 7.51 times higher than those who had been injured to the head due to gunshot, respectively. Even patients who had been injured to the head because of assault show much higher involvement in injury risk than non-assault patients (Odds Ratio = 8.46). These findings highlight the need for a large national study to confirm the findings. It also draws attention to the importance of public awareness and to special injury prevention programs that not only focus on saving lives and lessening the number of injuries, illnesses, and fatalities, but also to limit the social and economic burden of injury among adults in Northern Jordan.
Electronic Journal of Statistics, 2008
We consider various properties of Bayesian inferences related to repeated sampling interpretation... more We consider various properties of Bayesian inferences related to repeated sampling interpretations, when we have a proper prior. While these can be seen as particularly relevant when the prior is diffuse, we argue that it is generally reasonable to consider such properties as part of our assessment of Bayesian inferences. We discuss the logical implications for how repeated sampling properties should be assessed when we have a proper prior. We develop optimal Bayesian repeated sampling inferences using a generalized idea of what it means for a credible region to contain a false value and discuss the practical use of this idea for error assessment and experimental design. We present results that connect Bayes factors with optimal inferences and develop a generalized concept of unbiasedness for credible regions. Further, we consider the effect of reparameterizations on hpd-like credible regions and argue that one reparameterization is most relevant, when repeated sampling properties and the prior are taken into account.
Statistics & Probability Letters, 2012
In this paper, a class of distributions called the two-parameter weighted exponential distributio... more In this paper, a class of distributions called the two-parameter weighted exponential distributions is introduced (TWE). This new class of distributions generalizes the onesweighted exponential distributions (WE)-proposed by Gupta and Kundu (2009). The main properties of this new class of distributions are investigated. Several statistical properties and statistical inferences are then obtained and studied. Two real data sets of which one is a right censored data set were analyzed, and it is shown that in both two cases our model fits much better than WE or some other existing models.
Sankhya A, 2013
We consider the problem of estimating the sum of squared means when the data are independent valu... more We consider the problem of estimating the sum of squared means when the data are independent values from normal distributions with known variance and unknown, possibly different, means. This example has posed difficulties for many approaches to inference. We consider a Bayesian formulation with a diffuse proper prior and examine the consistency properties of several estimates derived from Bayesian considerations. We prove that a particular Bayesian estimate (LRSE) is consistent in a much wider set of circumstances than other Bayesian estimates like the posterior mean and mode. We show that the LRSE is either equal to the positive part of the UMVUE or differs from it with a relative error no greater than 2/n. We also prove a consistency result for interval estimation and discuss checking for prior-data conflict. We conclude that a general inference principle applied to this example leads to reasonable inferences and that there is not a problem with the Bayesian formulation or prior chosen.
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Papers by Mohammed Shakhatreh