REVSTAT-Statistical Journal

A Study on Zografos-Balakrishnan Log-Normal Distribution

D. S. Shibu — 2024-02-22

In this article, we studied a generalization of the log-normal distribution called Zografos-Balakrishnan log-normal distribution and investigate its various important properties and functions including moments, quantile function, various reliability measures, Rényi entropy, and some inequality measures. The estimation of unknown parameters is discussed by the methods of maximum likelihood, and the Bayesian technique and their simulation studies are also carried out. The applicability of the distribution is illustrated utilizing a real dataset. A likelihood ratio test is utilized for testing the efficiency of the third parameter. The effectiveness of this model for the dataset is also established using the parametric bootstrap approach.

Bounds on Negative Binomial Approximation to Call Function

Amit N. Kumar — 2024-02-22

In this paper, we develop Stein's method for negative binomial distribution using call function defined by f_z(k) = (k - z)⁺= max{k - z, 0}, for k ≥ 0 and z ≥ 0. We obtain error bounds between E [ f_z(N_r,p)] and E [ f_z(V )], where N_r,p follows negative binomial distribution and V is the sum of locally dependent random variables, using certain conditions on moments. We demonstrate our results through an interesting application, namely, collateralized debt obligation (CDO), and compare the bounds with the existing bounds.

Tales of the Wakeby Tail and Alternatives When Modelling Extreme Floods

Jesper Rydén — 2024-02-22

Estimation of return levels, based on extreme-value distributions, is of importance in the earth and environmental sciences. The selection of an appropriate probability distribution is crucial. The Wakeby distribution has shown to be an interesting alternative. By simulation studies, we investigate by various means of minimum distance to distinguish between common distributions when modelling extreme events in hydrology. Estimation of parameters is performed by L-moments. Moreover, time series of annual maximum floods from major unregulated rivers in Northern Sweden were analysed with respect to fitting an appropriate distribution. The results of the simulation study shows that the Wakeby distribution has the best fit of the tail for a wide range of sample sizes. For the analysis of extreme floods, the Wakeby distribution is in the majority of cases the best fit by means of minimum distance. However, when considering estimation of return levels by competing distributions, results can vary considerably for longer return periods.

On q-Generalized Extreme Values under Power Normalization with Properties, Estimation Methods and Applications to Covid-19 Data

Mohamed S. Eliwa — 2024-02-22

This paper introduces the q-analogues of the generalized extreme value distribution and its discrete counterpart under power normalization. The inclusion of the parameter q enhances modeling flexibility. The continuous extended model can produce various types of hazard rate functions, with supports that can be finite, infinite, or bounded above or below. Additionally, these new models can effectively handle skewed data, particularly those with highly extreme observations. Statistical properties of the proposed continuous distribution are presented, and the model parameters are estimated using various approaches. A simulation study evaluates the performance of the estimators across different sample sizes. Finally, three distinct real datasets are analyzed to demonstrate the versatility of the proposed model.

Identifiability Analysis Using Data Cloning

José Augusto Sartori Junior — 2024-02-22

Lack of identifiability in statistical models may hinder unique inferential conclusions. Therefore, the search for parametric constraints that ensure identifiability is of utmost importance in statistics. However, for complex modeling strategies, even acquiring the knowledge that the model is unidentifiable may prove very difficult. In this paper, we investigate the use of Data Cloning, a modern algorithm for classical inference in latent variable models, as a tool for assessing model identifiability. We discuss its advantages and disadvantages and illustrate its use with a dynamic linear model.

Analysis of Antibody Data Using Skew-normal and Skew-T Mixture Models

Tiago Dias Domingues — 2024-02-22

Gaussian mixture models, which assume a Normal distribution for each component, are popular in antibody (or serological) data analysis to help determining antibody-positive and antibody-negative individuals. In this work, we advocate using finite mixture models based on Skew-Normal and Skew-t distributions for serological data analysis. These flexible mixing distributions have the advantage of describing right and left asymmetry often observed in the distributions of known antibody-negative and antibody-positive individuals, respectively. We illustrate the application of these alternative mixture models in a data set on the role of human herpesviruses in the Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.

A Letter from the Editor-in-Chief

Manuel Scotto — 2024-02-22