Newdistns: An R Package for New Families of Distributions

The contributed R package Newdistns written by the authors is introduced. This package computes the probability density function, cumulative distribution function, quantile function, random numbers and some measures of inference for nineteen families of distributions. Each family is flexible enough to encompass a large number of structures. The use of the package is illustrated using a real data set. Also robustness of random number generation is checked by simulation

Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions

The generalization of the classical distributions is an old practice and has been considered as precious as many other practical problems in statistics. These generalizations started with the introduction of the additional location, scale or shape parameters. In the last couple of years, this branch of statistics has received a great deal of attention and quite a few new generalized classes of distributions have been introduced. We present a brief survey of this branch and introduce several new families as well

Some Characterizations of The Exponential Family

This paper introduces some characterizations concerning the exponential family. Recurrence relation between two consecutive conditional moments of h(z) given x<z<y  is presented. In addition, an    expression of V[h(Z]x<Z< y)as well as a closed form of E[hr(Z)x<Z< y] in terms of the failure rate and the reversed failure rate is deduced. Finally, the left rth truncated moment of h(Yk) ( where Yk is   the Kth order statistic) is expressed in terms of a polynomial,  h(-) , of degree r. Some results concerning the exponentiated Pareto, exponentiated Weibull, the Modified Weibull, Weibull, generalized exponential, Linear failure rate,1st type Pearsonian distributions, Burr, power and the uniform distributions are obtained as special cases

Studies on properties and estimation problems for modified extension of exponential distribution

The present paper considers modified extension of the exponential distribution with three parameters. We study the main properties of this new distribution, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modified- extension exponential distribution (MEXED) we have obtained the Bayes Estimators of scale and shape parameters using Lindley's approximation (L-approximation) under squared error loss function. But, through this approximation technique it is not possible to compute the interval estimates of the parameters. Therefore, we also propose Gibbs sampling method to generate sample from the posterior distribution. On the basis of generated posterior sample we computed the Bayes estimates of the unknown parameters and constructed 95 % highest posterior density credible intervals. A Monte Carlo simulation study is carried out to compare the performance of Bayes estimators with the corresponding classical estimators in terms of their simulated risk. A real data set has been considered for illustrative purpose of the study.Comment: 22,

Statistical modeling of skewed data using newly formed parametric distributions

Several newly formed continuous parametric distributions are introduced to analyze skewed data. Firstly, a two-parameter smooth continuous lognormal-Pareto composite distribution is introduced for modeling highly positively skewed data. The new density is a lognormal density up to an unknown threshold value and a Pareto density for the remainder. The resulting density is similar in shape to the lognormal density, yet its upper tail is larger than the lognormal density and the tail behavior is quite similar to the Pareto density. Parameter estimation methods and the goodness-of-fit criterion for the new distribution are presented. A large actuarial data set is analyzed to illustrate the better fit and applicability of the new distribution over other leading distributions. Secondly, the Odd Weibull family is introduced for modeling data with a wide variety of hazard functions. This three-parameter family is derived by considering the distributions of the odds of the Weibull and inverse Weibull families. As a result, the Odd Weibull family is not only useful for testing goodness-of-fit of the Weibull and inverse Weibull as submodels, but it is also convenient for modeling and fitting different data sets, especially in the presence of censoring and truncation. This newly formed family not only possesses all five major hazard shapes: constant, increasing, decreasing, bathtub-shaped and unimodal failure rates, but also has wide variety of density shapes. The model parameters for exact, grouped, censored and truncated data are estimated in two different ways due to the fact that the inverse transformation of the Odd Weibull family does not change its density function. Examples are provided based on survival, reliability, and environmental sciences data to illustrate the variety of density and hazard shapes by analyzing complete and incomplete data. Thirdly, the two-parameter logistic-sinh distribution is introduced for modeling highly negatively skewed data with extreme observations. The resulting family provides not only negatively skewed densities with thick tails, but also variety of monotonic density shapes. The advantages of using the proposed family are demonstrated and compared by illustrating well-known examples. Finally, the folded parametric families are introduced to model the positively skewed data with zero data values