Journal of Data Science

The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp–Leone random variable as a generator, called the Type II generalized Topp– Leone–G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.

We propose distributed generalized linear models for the purpose of incorporating lagged effects. The model class provides a more accurate statistical measure of the relationship between the dependent variable and a series of covariates. The estimators from the proposed procedure are shown to be consistent. Simulation studies not only confirm the asymptotic properties of the estimators, but exhibit the adverse effects of model misspecification in terms of accuracy of model estimation and prediction. The application is illustrated by analyzing the presidential election data of 2016.

In the linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components to parameterize the weight function. The formulation allows for efficient determination of tuning parameters and hence is computationally advantageous. Moreover, WOCR offers insights for deriving new better variants. Specifically, we advocate assigning weights to components based on their correlations with the response, which may lead to enhanced predictive performance. Both simulated studies and real data examples are provided to assess and illustrate the advantages of the proposed methods.

In this paper we use the maximum likelihood (ML) and the modified maximum likelihood (MML) methods to estimate the unknown parameters of the inverse Weibull (IW) distribution as well as the corresponding approximate confidence intervals. The estimates of the unknown parameters are obtained based on two sampling schemes, namely, simple random sampling (SRS) and ranked set sampling (RSS). Comparison between the different proposed estimators is made through simulation via their mean square errors (MSE), Pitman nearness probability (PN) and confidence length.

An exponentiated Weibull-geometric distribution is defined and studied. A new count data regression model, based on the exponentiated Weibull-geometric distribution, is also defined. The regression model can be applied to fit an underdispersed or an over-dispersed count data. The exponentiated Weibull-geometric regression model is fitted to two numerical data sets. The new model provided a better fit than the fit from its competitors.

In this article, a new family of lifetime distributions by adding an additional parameter to the existing distributions is introduced. The new family is called, the extended alpha power transformed family of distributions. For the proposed family, explicit expressions for some mathematical properties along with estimation of parameters through Maximum likelihood Method are discussed. A special sub-model, called the extended alpha power transformed Weibull distribution is considered in detail. The proposed model is very flexible and can be used to model data with increasing, decreasing or bathtub shaped hazard rates. To access the behavior of the model parameters, a small simulation study has also been carried out. For the new family, some useful characterizations are also presented. Finally, the potentiality of the proposed method is showen via analyzing two real data sets taken from reliability engineering and bio-medical fields.

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

A technique is proposed to estimate the conception rate using the distribution of first birth interval of recently married women. The proposed technique adjusts the truncation and selection effects present in a crosssectional data. Real data from NFHS-3 and NFHS-4 are used for illustration.

In this study we have considered different methods of estimation of the unknown parameters of a two-parameter unit-Gamma (UG) distribution from the frequentists point of view. First, we briefly describe different frequentists approaches: maximum likelihood estimators, moments estimators, least squares estimators, maximum product of spacings estimators, method of Cramer-von-Mises, methods of AndersonDarling and four variants of Anderson-Darling test and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their bias and root mean squared error using simulated samples. Also, for each method of estimation, we consider the interval estimation using the bootstrap method and calculate the coverage probability and the average width of the bootstrap confidence intervals. The study reveals that the maximum product of spacing estimators and Anderson-Darling 2 (AD2) estimators are highly competitive with the maximum likelihood estimators in small and large samples. Finally, two real data sets have been analyzed for illustrative purposes.

In this paper, parameters estimation for the generalized Rayleigh (GR) distribution are discussed under the adaptive type-II progressive censoring schemes based on maximum product spacing. A comparison studies with another methods as maximum likelihood, and Bayesian estimation by use Markov chain Monte Carlo (MCMC) are discussed. Also, reliability estimation and hazard function are obtained. A numerical study using real data and Monte Carlo Simulation are performed to compare between different methods.