Statistica

Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes

Xiaofei Xu, Zhengze Li, Masanobu Taniguchi — Tue, 12 Jul 2022 00:00:00 +0200

For Gaussian stationary processes, the likelihood functions include the inverse and determinant of the covariance matrices, and Whittle likelihood is considered as a standard technique to avoid expensive matrix determinant and inversions under large sample size. In this paper, we investigate the difference between the exact likelihood and Whittle likelihood with finite sample size for moving average processes of order one. We elucidate the theoretical expressions of two likelihood functions and their expectations and evaluate the performance between exact likelihood and Whittle likelihood numerically. We find that the exact likelihood and Whittle likelihood perform similarly when the true value of parameter is close to zero, while the difference becomes large and Whittle estimator performs poorly when absolute value of parameter gets close to one. This is an important warning when we use the Whittle likelihood and estimator if the parameter of moving average process nears the boundary of parameter space.

On a Bivariate XGamma Distribution Derived from Copula

Mohammed Abulebda, Ashok Kumar Pathak, Arvind Pandey, Shikhar Tyagi — Tue, 12 Jul 2022 00:00:00 +0200

In this paper, a new bivariate XGamma (BXG) distribution is presented using Farlie-Gumbel-Morgenstern (FGM) copula. We derive the expressions for conditional distribution, regression function and product moments for the BXG distribution. Concept of reliability and various measures of local dependence are also studied for the proposed model. Furthermore, estimation of the parameters of the BXG distribution is obtained through maximum likelihood estimation and inference function of margin estimation procedures. Finally, an application of the same is also demonstrated to a real data set.

A Note on Fibonacci Sequences of Random Variables

Ismihan Bayramoğlu — Tue, 12 Jul 2022 00:00:00 +0200

The aim of this paper is to introduce and investigate the newrandom sequence in the form{X₀, X₁, X_n = X_n−2 +X_n−1, n = 2, 3, ..˙} , referred to as Fibonacci Sequence of Random Variables (FSRV). The initial random variables X₀ and X₁ are assumed to be absolutely continuous with joint probability density function (pdf) f_X0,X1 . The FSRV is completely determined by X₀ and X₁ and the members of Fibonacci sequence F ≡ {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...}. We examine the distributional and limit properties of the random sequence X_n, n = 0, 1, 2, ... .

A Note on Estimation of Stress-Strength Reliability under Generalized Uniform Distribution when Strength Stochastically Dominates Stress

Manisha Pal — Tue, 12 Jul 2022 00:00:00 +0200

In this note we find the UMVUE and a consistent estimator of the stress strength reliability of a system, whose strength stochastically dominates the stress. Strength of the system and the stress on it are assumed to be independently distributed, each having a generalized uniformdistribution. Simulation study has been carried out, and an application to real life data has also been cited.

Comments on Irshad et al. (2021) “The Zografos-Balakrishnan Lindley Distribution: Properties and Applications”

Hamid Ghorbani, Muhammed Rasheed Irshad — Tue, 12 Jul 2022 00:00:00 +0200

This paper corrects and updates Irshad et al. (2021) by some technical comments. The original paperwas inadvertently published with some errors, mainly the computational ones regarding the maximum likelihood (ML) estimate of the parameters of the fitted models which will be addressed and corrected in this paper. Furthermore, the standard errors of the ML estimates of different fitted models, as an important indicator of the accuracy of estimates and particularly are necessary for making the statistical inference for the population parameters, have been added.