Mathematics

In this paper we defined a new lifetime model called the the Exponentiated additive Weibull (EAW) distribution. The proposed distribution has a number of well-known lifetime distributions as special submodels, such as the additive Weibull, exponentiated modified Weibull, exponentiated Weibull and generalized linear failure rate distributions among others. We obtain quantile, moments, moment generating functions, incomplete moment, residual life and reversed Failure Rate Functions, mean deviations, Bonferroni and Lorenz curves. The method of maximum likelihood is used for estimating the model parameters. Applications illustrate the potentiality of the proposed distribution.

In this paper, a method for generating a new family of univariate continuous distributions using the tangent function is proposed. Some general properties of this new family are discussed: hazard function, quantile function, Rényi and Shannon entropies, symmetry, and existence of the non-central ℎ moment. Some new members as sub-families in the − family of distributions are provided. Three members of the new subfamilies are defined and discussed: the four-parameter Normal-Generalized hyperbolic secant distribution (), the four-parameter Gumbel-Generalized hyperbolic secant distribution (), and the fiveparameter Generalized Error-Generalized hyperbolic secant distribution (), the shapes of these distributions were found: skewed right, skewed left, or symmetric, and unimodal, bimodal, or trimodal. Finally, to demonstrate the usefulness and the capability of the distributions, two real data sets are used and the results are compared with other known distributions.

We introduce a new class of continuous distributions called the generalized odd Lindley-G family. Four special models of the new family are provided. Some explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi and Shannon entropies are derived. The maximum likelihood method is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. W...

In this paper, a new probability distribution, which is synthesized based on the quasi xgamma [26] and geometric distributions, is proposed and studied. The proposed distribution so synthesized is basically a family of positively skewed probability distributions and possesses increasing and decreasing hazard rate properties depending on the values of the unknown parameters. Different important distributional and survival and/or reliability properties are also studied. A unique characterization of the distribution is presented based on reversed hazard rate. Seven different frequentist methods of estimating unknown parameters are proposed and the methods are justified with Monte-Carlo simulation study. Flexible data generation algorithm eases the utility of the proposed model in survival and/or reliability application which is accomplished by real data analyses and by comparing with other competitive life distributions.

For a given data set the problem of selecting either Lindley or xgamma distribution with unknown parameter is investigated in this article. Both these distributions can be used quite effectively for analyzing skewed non-negative data and in modeling time-to-event data sets. We have used the ratio of the maximized likelihoods in choosing between the Lindley and xgamma distributions. Asymptotic distributions of the ratio of the maximized likelihoods are obtained and those are utilized to determine the minimum sample size required to discriminate between these two distributions for user specified probability of correct selection and tolerance limit.

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fi...

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set.

In this paper, a new two-parameter model called generalized Ramos-Louzada (GRL) distribution is proposed. The new model provides more flexibility in modeling data with increasing, decreasing, j shaped and reversed-J shaped hazard rate function. Several statistical and reliability properties of the GRL model are also presented in this paper. The unknown parameters of the GRL distribution are discussed using eight frequentist estimation approaches. These approaches are important to develop a guideline to choose the best method of estimation for the GRL parameters, that would be of great interest to practitioners and applied statisticians. A detailed numerical simulation study is carried out to examine the bias and the mean square error of the proposed estimators. We illustrate the performance of the GRL distribution using two real data sets from the fields of medicine and geology and both data sets show that the new model is more appropriate as compared to the gamma, Marshall-Olkin ex...

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing...

The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its different distributional properties. To estimate the unknown parameter, maximum likelihood method is proposed. A Monte-Carlo simulation study is performed to understand the behaviour of the estimates for varying sample size. To illustrate the application of the proposed distribution, a real data set on the long axis orientation of feldspar laths in basalt rock is analyzed and compared with other circular distributions.

Abstract—Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits a...