Generalized modified slash distribution with applications

Abstract

In this article a generalization of the modified slash distribution is introduced. This model is based on the quotient of two independent random variables, whose distributions are a normal and a one-parameter gamma, respectively. The resulting distribution is a new model whose kurtosis is greater than other slash distributions. The probability density function, its properties, moments, and kurtosis coefficient are obtained. Inference based on moment and maximum likelihood methods is carried out. The multivariate version is also introduced. Two real data sets are considered in which it is shown that the new model fits better to symmetric data with heavy tails than other slash extensions previously introduced in literature.     

A generalized skew slash distribution via gamma-normal distribution

In this article, we introduce a generalization of the slash distribution via the gamma-normal distribution. We define the new slash distribution by relation of a gamma-normal random variable with respect to a power of a uniform random variable. The newly defined distribution generalizes the slash distribution and is more flexible in terms of its kurtosis and skewness than the slash distribution. Basic properties of the new distribution are studied. We derive the maximum likelihood estimators of its parameters and apply the distribution to a real dataset.     

A new family of multivariate skew slash distribution

In this article, the new family of multivariate skew slash distribution is defined. According to the definition, a stochastic representation of the multivariate skew slash distribution is derived. The first four moments and measures of skewness and kurtosis of a random vector with the multivariate skew slash distribution are obtained. The distribution of quadratic forms for the multivariate skew slash distribution and the non central skew slash χ² distribution are studied. Maximum likelihood inference and real data illustration are discussed. In the end, the potential extension of multivariate skew slash distribution is discussed.     

Modified slashed generalized exponential distribution

Abstract

In this article, we introduce a new distribution for modeling positive data sets with high kurtosis, the modified slashed generalized exponential distribution. The new model can be seen as a modified version of the slashed generalized exponential distribution. It arises as a quotient of two independent random variables, one being a generalized exponential distribution in the numerator and a power of the exponential distribution in the denominator. We studied various structural properties (such as the stochastic representation, density function, hazard rate function and moments) and discuss moment and maximum likelihood estimating approaches. Two real data sets are considered in which the utility of the new model in the analysis with high kurtosis is illustrated.     

Slashed generalized exponential distribution

In this paper, we introduce an extension of the generalized exponential (GE) distribution, making it more robust against possible influential observations. The new model is defined as the quotient between a GE random variable and a beta-distributed random variable with one unknown parameter. The resulting distribution is a distribution with greater kurtosis than the GE distribution. Probability properties of the distribution such as moments and asymmetry and kurtosis are studied. Likewise, statistical properties are investigated using the method of moments and the maximum likelihood approach. Two real data analyses are reported illustrating better performance of the new model over the GE model.     

A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations.     

Modified skew-slash distribution

Abstract

In this work, we introduce a new skewed slash distribution. This modification of the skew-slash distribution is obtained by the quotient of two independent random variables. That quotient consists on a skew-normal distribution divided by a power of an exponential distribution with scale parameter equal to two. In this way, the new skew distribution has a heavier tail than that of the skew-slash distribution. We give the probability density function expressed by an integral, but we obtain some important properties useful for making inferences, such as moment estimators and maximum likelihood estimators. By way of illustration and by using real data, we provide maximum likelihood estimates for the parameters of the modified skew-slash and the skew-slash distributions. Finally, we introduce a multivariate version of this new distribution.     

Wrapped Lindley distribution

In this article, we introduce a new circular distribution to be called as wrapped Lindley distribution and derive expressions for characteristic function, trigonometric moments, coefficients of skewness, and kurtosis. Method of maximum likelihood estimation is used for the estimation of parameters. We carry out a simulation study to show that the obtained maximum likelihood estimator is consistent. The proposed model is also applied to a real-life dataset, and its performance is compared with that of wrapped exponential distribution.     

A skew extension of the slash distribution via beta-normal distribution

In this work we introduce a generalization of the slash distribution using beta-normal distribution. This newly defined generalization is more flexible than the ordinary slash distribution and contains distributions that can be not only symmetric and unimodal, but also asymmetric and bimodal. We study the properties of the new generalized distribution and demonstrate its use on some real data sets considering maximum likelihood estimation procedure.     

Modified slashed-Rayleigh distribution

A new family of slash distributions, the modified slashed-Rayleigh distribution, is proposed and studied. This family is an extension of the ordinary Rayleigh distribution, being more flexible in terms of distributional kurtosis. It arises as a quotient of two independent random variables, one being a Rayleigh distribution in the numerator and the other a power of the exponential distribution in denominator. We present properties of the proposed family. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Finally, we conduct a small-scale simulation study to evaluate the performance of the maximum likelihood estimators and apply the results to a real data set, revealing its good performance.     

A generalization of the multivariate slash distribution

In this paper, we propose a generalization of the multivariate slash distribution and investigate some of its properties. We show that the new distribution belongs to the elliptically contoured distributions family, and can have heavier tails than the multivariate slash distribution. Therefore, this generalization of the multivariate slash distribution can be considered as an alternative heavy-tailed distribution for modeling data sets in a variety of settings. We apply the generalized multivariate slash distribution to two real data sets to provide some illustrative examples.     

An extension of the generalized linear failure rate distribution

In this article, we introduce a new extension of the generalized linear failure rate (GLFR) distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and GLFR distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function (hrf) depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hrf, and reversible hrf. The maximum likelihood estimation of the parameters is also discussed. At the end, a real dataset is given to illustrate the usefulness of this new distribution in analyzing lifetime data.     

An Alpha Half Normal Slash Distribution for Analyzing Non Negative Data

In this paper, we study a new class of slash distribution. We define the distribution through means of a stochastic representation as the mixture of an alpha half normal random variable with respect to the power of a uniform random variable. Properties involving moments and moment generating function are derived. The usefulness and flexibility of the proposed distribution is illustrated through a real application by maximum likelihood procedure.     

An extension of the half-normal distribution

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.     

Uniform-Geometric distribution

In this paper, a new discrete distribution called Uniform-Geometric distribution is proposed. Several distributional properties including survival function, moments, skewness, kurtosis, entropy and hazard rate function are discussed. Estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square error. Two real data applications are also presented to see that new distribution is useful in modelling data.     

Bivariate Kumaraswamy distribution: properties and a new method to generate bivariate classes

In this paper, we introduce a bivariate Kumaraswamy (BVK) distribution whose marginals are Kumaraswamy distributions. The cumulative distribution function of this bivariate model has absolutely continuous and singular parts. Representations for the cumulative and density functions are presented and properties such as marginal and conditional distributions, product moments and conditional moments are obtained. We show that the BVK model can be obtained from the Marshall and Olkin survival copula and obtain a tail dependence measure. The estimation of the parameters by maximum likelihood is discussed and the Fisher information matrix is determined. We propose an EM algorithm to estimate the parameters. Some simulations are presented to verify the performance of the direct maximum-likelihood estimation and the proposed EM algorithm. We also present a method to generate bivariate distributions from our proposed BVK distribution. Furthermore, we introduce a BVK distribution which has only an absolutely continuous part and discuss some of its properties. Finally, a real data set is analysed for illustrative purposes.     

Moments of truncated normal/independent distributions

In this work we have considered the problem of finding the moments of a doubly truncated member of the class of normal/independent distributions. We obtained a general result and then use it to derive the moments in the case of doubly truncated versions of Pearson type VII distribution, slash distribution, contaminated normal distribution, double exponential distribution and variance gamma distribution. We also give an application of some actuarial data.     

Slashed power-Lindley distribution

In this article, we introduce the slashed power-Lindley distribution. This model can be seen as an extension of the power-Lindley distribution with more flexibility in terms of the kurtosis of distribution. It arises as the ratio of two independent random variables, the one being a power-Lindley distribution and a power of the uniform distribution. We present properties and carry out estimates of the model parameters by the maximum likelihood method. Finally, we conduct a small simulation study to evaluate the performance of maximum likelihood estimators and we analyze a real data set to illustrate the usefulness of the new model.     

Inverse Weibull power series distributions: properties and applications

Inverse Weibull (IW) distribution is one of the widely used probability distributions for nonnegative data modelling, specifically, for describing degradation phenomena of mechanical components. In this paper, by compounding IW and power series distributions we introduce a new lifetime distribution. The compounding procedure follows the same set-up carried out by Adamidis and Loukas [A lifetime distribution with decreasing failure rate. Stat Probab Lett. 1998;39:35–42]. We provide mathematical properties of this new distribution such as moments, estimation by maximum likelihood with censored data, inference for a large sample and the EM algorithm to determine the maximum likelihood estimates of the parameters. Furthermore, we characterize the proposed distributions using a simple relationship between two truncated moments and maximum entropy principle under suitable constraints. Finally, to show the flexibility of this type of distributions, we demonstrate applications of two real data sets.     

A generalization of the slashed distribution via alpha skew normal distribution

Statistical Methods & Applications - In this paper, we introduce a new class of the slash distribution, an alpha skew normal slash distribution. The proposed model is more flexible in terms of...