Authors:Ingwer Borg, Patrick Mair Pages: 1 - 9 Abstract: When comparing two or more multidimensional scaling (MDS) configurations, one usually first eliminates meaningless differences by Procrustean transformations. Such fittings lead to a number of unresolved issues such as the typical shrinkage of the fitted configuration relative to the target or how to interpret major similarity measures under various conditions of noise in the data. We here prove that the shrinkage ratio is equivalent to the correlation of the coordinates of the target and the fitted configuration. Thus, in real-life applications, the fitted configuration is always smaller than the target configuration. Both coefficients approach 0 as the noise level goes up. The congruence coefficient of the configurations' distances, in contrast, remains at a high level even in case of pure noise, falsely suggesting that the configurations are somewhat similar. This is important information for the user of Procrustean analyses. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1423 Issue No:Vol. 51, No. 4 (2022)

Authors:Dipak Patil, U. V. Naik-Nimbalkar, M. M. Kale Pages: 10 - 34 Abstract: We consider an expression for the probability R=P(Y<X) where the random variables X and Y denote strength and stress, respectively. Our aim is to study the effect of the dependency between X and Y on R. We assume that X and Y follow exponential distributions and their dependency is modeled by a copula with the dependency parameter theta. We obtain a closed-form expression for R for Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate exponential copulas and compute R for Gumbel-Hougaard (GH) copula using a Monte-Carlo integration technique. We plot a graph of R versus theta to study the effect of dependency on R. We estimate R by plugging in the estimates of the marginal parameters and theta in its expression. The estimates of the marginal parameters are based on the marginal likelihood. The estimates of theta are obtained from two different methods; one is based on the conditional likelihood and the other on the method of moments using Blomqvist's beta. Asymptotic distribution of both the estimators of R is obtained. For illustration purpose, we apply our results to a real data set. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1293 Issue No:Vol. 51, No. 4 (2022)

Authors:Hossein Pasha-Zanoosi, Ahmad Pourdarvish, Akbar Asgharzadeh Pages: 35 - 59 Abstract: This article deals with the problem of reliability in a multicomponent stress-strength (MSS) model when both stress and strength variables are from exponentiated Teissier (ET) distributions. The reliability of the system is determined using both classical and Bayesian methods, based on two scenarios where the common scale parameter is unknown or known. In the first scenario, where the common scale parameter is unknown, the maximum likelihood estimation (MLE) and the approximate Bayes estimation are derived. In the second scenario, where the scale parameter is known, the MLE, the uniformly minimum variance unbiased estimator (UMVUE) and the exact Bayes estimation are obtained. In the both scenarios, the asymptotic confidence interval and the highest probability density credible interval are established. Furthermore, two other asymptotic confidence intervals are computed based on the Logit and Arcsin transformations. Monte Carlo simulations are implemented to compare the different proposed methods. Finally, one real example is presented in support of suggested procedures. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1327 Issue No:Vol. 51, No. 4 (2022)

Authors:Proloy Banerjee, Shreya Bhunia Pages: 60 - 75 Abstract: In this article a generalization of the inverse Rayleigh distribution has been addressed by using DUS transformation, named as Exponential Transformed Inverse Rayleigh (ETIR) distribution. Some of the statistical properties of this newly proposed distribution like mode, quantiles, moment, moment generating function, survival and hazard rate function have been studied comprehensively. To estimate the parameter of this distribution, four different estimation procedures, such as maximum likelihood estimation (MLE), maximum product spacing method (MPS), least square method (LSE) and weighted least square method (WLSE) are briefly discussed. Performance of these estimates are compared using extensive simulations. As an application point of view the model superiority is verified through two real datasets. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1338 Issue No:Vol. 51, No. 4 (2022)

Authors:Christian Bruch, Barbara Felderer Pages: 76 - 95 Abstract: The multilevel and poststratification approach is commonly used to draw valid inference from (non-probabilistic) surveys. This Bayesian approach includes varying regression coefficients for which prior distributions of their variance parameter must be specified. The choice of the distribution is far from being trivial and many contradicting recommendations exist in the literature. The prior choice may be even more challenging when data results from a highly selective inclusion mechanism, such as applied by volunteer panels. We conduct a Monte Carlo simulation study to evaluate the effect of different distribution choices on bias in the estimation of a proportion based on a sample that is subject to a highly selective inclusion mechanism. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1361 Issue No:Vol. 51, No. 4 (2022)

Authors:Saidat Fehintola Olaniran, Mohd Tahir Ismail Pages: 96 - 119 Abstract: Several authors have studied fractional cointegration in time series data, but little or no consideration has been extended to panel data settings. Therefore, in this paper, we compare the finite sample behaviour of existing fractional cointegration time-series test procedures in panel data settings. This comparison is performed to determine the best tests that can be adapted to fractional cointegration in panel data settings. Specifically, simulation studies and real-life data analysis were performed to study the changes in the empirical type I error rate and power of six semiparametric fractional cointegration tests in panel settings. The various results revealed the limitations of the tests in the nonstationary and low or high correlation of the residual errors conditions. Also, two of the test procedures were recommended for testing the null hypothesis of no fractional cointegration in both time series and panel data settings. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1170 Issue No:Vol. 51, No. 4 (2022)

Authors:Farouq Mohammad A. Alam Pages: 120 - 147 Abstract: In statistical literature, various probability distributions exist with advantageous properties, while others are considered pathological since their properties are counterintuitive. A well-known pathological probability distribution is the Cauchy distribution, and it has applications in areas related to environmental and financial research. Both the log-Cauchy and half-Cauchy distributions, which have close connections to the Cauchy distribution, are pathological distributions. This paper considers another pathological model called the Cauchy Birnbaum-Saunders distribution. Some of the statistical properties of this distribution are discussed briefly, and its parameters are estimated using eight frequentist estimation methods, including the maximum likelihood, least-squares-based, and minimum distance estimation methods. Monte Carlo simulations are carried out to compare and examine the performance of each estimator numerically. Furthermore, a recent climate data set is analyzed to show the practical applicability of this model. PubDate: 2022-08-26 DOI: 10.17713/ajs.v51i4.1331 Issue No:Vol. 51, No. 4 (2022)