A discrete analogue of odd Weibull-G family of distributions: properties, classical and Bayesian estimation with applications to count data.

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets.

A one-parameter discrete distribution for over-dispersed data: statistical and reliability properties with applications.

In the literature of distribution theory, a vast proportion is acquired by discrete distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing discrete models. In view of this, we propose a new flexible discrete distribution with one parameter. Some statistical and reliability are derived. These properties can be expressed as closed-forms. One of the important virtues of this newly evolved model is that it can model not only over-dispersed, positively skewed and leptokurtic data sets, but it can also be utilized for modeling increasing, decreasing and unimodal failure rate. Various estimation approaches are utilized to estimate the model parameter. A simulation study is carried out to examine the performance of the estimators for different sample size. The flexibility of the new model for analyzing different types of data is explained by utilizing four real data sets in different fields. Finally, the proposed model can serve as an alternative model to other distributions in the existing literature for modeling positive real data in several areas.

A new statistical approach to model the counts of novel coronavirus cases.

This study proposes new statistical tools to analyze the counts of the daily coronavirus cases and deaths. Since the daily new deaths exhibit highly over-dispersion, we introduce a new two-parameter discrete distribution, called discrete generalized Lindley, which enables us to model all kinds of dispersion such as under-, equi-, and over-dispersion. Additionally, we introduce a new count regression model based on the proposed distribution to investigate the effects of the important risk factors on the counts of deaths for OECD countries. Three data sets are analyzed with proposed models and competitive models. Empirical findings show that air pollution, the proportion of obesity, and smokers in a population do not affect the counts of deaths for OECD countries. The interesting empirical result is that the countries with having higher alcohol consumption have lower counts of deaths.

Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution.

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton-Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model.

Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications.

In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean time to failure, mean time between failure, availability and reliability function of consecutive linear and circular systems are studied. The hazard rate function can be increasing, decreasing, unimodal-bathtub, unimodal, bathtub, J and inverse J-shaped depending on its parameters values. After introducing the general class, two special models of the new family are discussed in detail. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. We also illustrate the importance of the new family by means of two distinctive real data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive and negative real data in many areas.

A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models.

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution.

This paper describes a method for computing estimates for the location parameter µ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (µ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.

A new one-parameter lifetime distribution and its regression model with applications.

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications.

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress-strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing-increasing-decreasing, increasing-decreasing-increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas.

Inference of progressively type-II censored competing risks data from Chen distribution with an application.

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation-maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

The introduction of breast milk donation in a Muslim country.

Breast milk donation (wet-nursing) for full-term babies is a well-known practice in Kuwait, but it has never been organized formally in a neonatal intensive care unit (NICU) for preterm babies. Donor milk banking as conducted in Western society is not considered to be ethical in Muslim society, where the milk donor and the recipient are required to know each other. Human milk is known to decrease the incidence of necrotizing enterocolitis; improve host defenses, digestion, absorption of nutrients, gastrointestinal function, and neurodevelopment of the child; and contribute to maternal physical and psychological well-being. A culturally accepted approach to donor milk banking is proposed as a means of overcoming the ethical issues surrounding milk donation in Muslim society. This report addresses the first step in raising awareness of the valuable contribution of donor milk to preterm babies and the organization of human milk donation for use in an NICU.

newborn requiring selective left bronchial intubation Case report

Pulmonary interstitial emphysema [PIE] is an iatrogenic pulmonary condition of the premature infant with immature lungs. PIE occurs almost exclusively with mechanical ventilation. We report a case of preterm newborn 26 weeks gestation who developed PIE in the right lung while on advanced nasal CPAP ventilation mode and managed by selective left bronchial intubation and mechanical ventilation