Family Of Univariate Distributions Research Articles

The Inverse Weibull Generator of Distributions: Properties and Applications

In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

A new extreme value copula and new families of univariate distributions based on Freund’s exponential model

Abstract The use of the exponential distribution and its multivariate generalizations is extremely popular in lifetime modeling. Freund’s bivariate exponential model (1961) is based on the idea that the remaining lifetime of any entity in a bivariate system is shortened when the other entity defaults. Such a model can be quite useful for studying systemic risk, for instance in financial systems. Guzmics and Pflug (2019) revisited Freund’s model, deriving the corresponding bivariate copula and examined some characteristics of it; furthermore, we opened the door for a multivariate setting. Now we present further investigations in the bivariate model: we compute the tail dependence coefficients, we examine the marginal and joint distributions of the componentwise maxima, which leads to an extreme value copula, which – to the best of our knowledge – has not been investigated in the literature yet. The original bivariate model of Freund has been extended to more variables by several authors. We also turn to the multivariate setting, and our focus is different from that of the previous generalizations, and therefore it is novel: examining the distribution of the sum and of the average of the lifetime variables (provided that the shock parameters are all the same) leads to new families of univariate distributions, which we call Exponential Gamma Mixture Type I and Type II (EGM) distributions. We present their basic properties, we provide asymptotics for them, and finally we also provide the limiting distribution for the EGM Type II distribution.

Risk Measures of the ERNB Distribution Generated by G-NB Family

This paper provides VaR and CVaR risk measures, calculated for the Erlang-Negative Binomial (ERNB) distribution. The Erlang and negative binomial distributions are given and then ERNB distribution is obtained using a family of univariate distributions which is called G-Negative Binomial (G-NB). It is defined as compounding the negative binomial distribution (NB) with any continuous distribution (G). Here, we use the ERNB distribution obtained as taking Erlang distribution instead of G. In this paper, we focus on the estimation of VaR and CVaR risk measures for this distribution in closed form and the explicit expressions are also presented for some parameter values. The results are portrayed in the figures. In additionally, numerical examples are given to illustrate changing of the risk measure according to some parameters on a real data set of automobile insurance policies.

A Generalized Gamma-Weibull Distribution: Model, Properties and Applications

We propose a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized Gamma-Weibull (GGW) distribution is studied as a special case of this family. Results for moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distributions of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution is shown via an application.

Some Properties of Gamma Generated Distributions

Based on standard probability distributions, new families of univariate distributions have been introduced and their properties studied by many authors. The present paper investigates some general properties of a family of Gamma generated distributions proposed by Zografos and Balakrishnan (2009).

Fitting Distributions with the Polyhazard Model with Dependence

The polyhazard model with dependent causes, first introduced to fit lifetime data, generalized the traditional polyhazard model by allowing the latent causes of failure to be dependent by using copula functions. When modeling lifetime data, marginal distributions are supported on the positive reals. Dropping this restriction, the method generates a rich family of univariate distributions with asymmetries and multiple modes. We show that this new family of distributions is able to approximate other distributions proposed in the literature, such as the generalized beta-generated distributions. These distributions are fitted to three real data sets.

A Reverse Engineering Approach to the Suppression of Citation Biases Reveals Universal Properties of Citation Distributions

The large amount of information contained in bibliographic databases has recently boosted the use of citations, and other indicators based on citation numbers, as tools for the quantitative assessment of scientific research. Citations counts are often interpreted as proxies for the scientific influence of papers, journals, scholars, and institutions. However, a rigorous and scientifically grounded methodology for a correct use of citation counts is still missing. In particular, cross-disciplinary comparisons in terms of raw citation counts systematically favors scientific disciplines with higher citation and publication rates. Here we perform an exhaustive study of the citation patterns of millions of papers, and derive a simple transformation of citation counts able to suppress the disproportionate citation counts among scientific domains. We find that the transformation is well described by a power-law function, and that the parameter values of the transformation are typical features of each scientific discipline. Universal properties of citation patterns descend therefore from the fact that citation distributions for papers in a specific field are all part of the same family of univariate distributions.

Properties of Coherent Systems with Dependent Components

We introduce two new families of univariate distributions that we call hyperminimal and hypermaximal distributions. These families have interesting applications in the context of reliability theory in that they contain that of coherent system lifetime distributions. For these families, we obtain distributions, bounds, and moments. We also define the minimal and maximal signatures of a coherent system with exchangeable components which allow us to represent the system distribution as generalized mixtures (i.e., mixtures with possibly negative weights) of series and parallel systems. These results can also be applied to order statistics (k-out-of-n systems). Finally, we give some applications studying coherent systems with different multivariate exponential joint distributions.

Multiparameter Univariate Bayesian Analysis

Abstract Bayesian analysis using Monte Carlo integration is a powerful method for univariate inference. This approach makes possible multiparameter flexibility within families of univariate distributions. These distributions are defined in this article by increasing spline functions superimposed on probability paper coordinate systems. Smoothing is controlled by the prior distribution. The prior distribution also can express uncertainties about the form of the tails when extrapolation beyond the range of the data is required. The handling of difficult forms of data (e.g., quantal response data) is straightforward. Posterior distributions for functions of the parameters can be easily computed.

Multiparameter Univariate Bayesian Analysis

Abstract Bayesian analysis using Monte Carlo integration is a powerful method for univariate inference. This approach makes possible multiparameter flexibility within families of univariate distributions. These distributions are defined in this article by increasing spline functions superimposed on probability paper coordinate systems. Smoothing is controlled by the prior distribution. The prior distribution also can express uncertainties about the form of the tails when extrapolation beyond the range of the data is required. The handling of difficult forms of data (e.g., quantal response data) is straightforward. Posterior distributions for functions of the parameters can be easily computed.