Bayesian Analysis of Record Statistics Based on Generalized Inverted Exponential Model, Hassan, Amal Soliman, Marwa Abd-Allah, and Nagy H. F. , International Journal of Advanced Science Engineering and Information Technology, Volume 8, Issue 2, p.323-335, (2018)
On the Inverse Power Lomax Distribution, Hassan, Amal Soliman, and Abd-Allah Marwa , Annals of Data Science, p.1-22, (2018)
Exponentiated Weibull-Lomax Distribution: Properties and Estimation., Hassan, Amal Soliman, and Marwa Abd-Allah , Journal of Data Science, Volume 16, Issue 2, p.277-298, (2018) Abstract

Abstract: In this article, we introduce a new class of five-parameter model called the Exponentiated Weibull Lomax arising from the Exponentiated Weibull generated family. The new class contains some existing distributions as well as some new models. Explicit expressions for its moments, distribution and density functions, moments of residual life function are derived. Furthermore, Rényi and q-entropies, probability weighted moments, and order statistics are obtained. Three suggested procedures of estimation, namely, the maximum likelihood, least squares and weigthed least squares are used to obtain the point estimators of the model parameters. Simulation study is performed to compare the performance of different estimates in terms of their relative biases and standard errors. In addition, an application to two real data sets demonstrate the usefulness of the new model comparing with some new models.

Estimation of (P Y< X) Using Record Values from the Generalized Inverted Exponential Distribution, Hassan, Amal Soliman, Marwa Abd-Allah, and Nagy Heba F. , Pakistan Journal of Statistics and Operation Research, Volume 14, Issue 3, p.645-660, (2018) Abstract

This article deals with the estimation of R = P(Y < X) when X and Y are distributed as two independent
generalized inverted exponential with common scale parameter and different shape parameters. The
maximum likelihood and Bayesian estimators of R are obtained on the basis of upper record values and
upper record ranked set samples. The Bayesian estimator cannot be obtained in explicit form, and therefore
it has been achieved using Lindley approximation. Simulation study is performed to compare the reliability
estimators in each record sampling scheme with respect to biases and mean square errors.

Exponentiated Lomax Geometric Distribution: Properties and Applications, Hassan, Amal Soliman, and Abdelghafar Marwa Abdallah , Pakistan Journal of Statistics and Operation Research, Volume 13, Issue 3, (2017) Abstract

In this paper, a new four-parameter lifetime distribution, called the exponentiated Lomax geometric (ELG) is introduced. The new lifetime distribution contains the Lomax geometric and exponentiated Pareto geometric as new sub-models. Explicit algebraic formulas of probability density function, survival and hazard functions are derived. Various structural properties of the new model are derived including; quantile function, Re'nyi entropy, moments, probability weighted moments, order statistic, Lorenz and Bonferroni curves. The estimation of the model parameters is performed by maximum likelihood method and inference for a large sample is discussed. The flexibility and potentiality of the new model in comparison with some other distributions are shown via an application to a real data set. We hope that the new model will be an adequate model for applications in various studies.

Optimum Group Limits for Maximum Likelihood Estimation of the Exponentiated Fréchet Distribution Based on Grouped Data, Marwa, A. A., Hegazy Zaher, and Elsherpieny E. A. , British Journal of Applied Science & Technology, Volume 3, Issue 4, p.1464-1480, (2013) Abstract

In many situations, instead of a complete sample, data are available only in grouped form.
In this situation the values of individual observations are not known, but the number of
observations that fall in each group is only known. Here the model under consideration is
the exponentiated Fréchet distribution. The aim of this paper is finding the MLE's for the
parameters of the exponentiated Fréchet distribution based on grouped data. The
asymptotic variance-covariance matrix has been derived and computed numerically.
Optimal group limits in the case unequi-spaced groupings so as to have a maximum
asymptotic relative efficiency are worked out.