Abstract: A new family of continuous distributions called the X-exponential-G (XE-G) family is proposed. Explicit expressions are derived for the ordinary and incomplete moments, generating functions, mean deviation about the mean and median, Shannon and R\'{e}nyi entropies, and order statistics of this new family. Estimation of the parameters of the new family is done using the method of maximum likelihood. Assessment of the performance of the maximum likelihood estimates is carried out through a simulation study using the quantile function of the XE-G distribution. The usefulness of this new family is illustrated by modeling two real datasets. PubDate: Sat, 02 Mar 2024 01:31:41 +000

Abstract: Four approximate F- tests derived by Fai and Cornelious in 1996 to make inference for fixed effects in mixed linear models of rank greater than one. Two of these approaches derived by introducing a Wald-type statistic distributed approximately as an F distribution, and the denominator degrees of freedom computed by matching the approximated one moment of the Wald-type statistic with the exact one moment of the F distribution. The other two approaches were derived by introducing a scaled Wald-type statistic to be distributed approximately as an F distribution, and the denominator degrees of freedom and the scale factor computed by matching the two moments of the statistic with the moments of the F distribution. This paper proposes two more approximate F-tests analogous to the four approaches where an adjusted estimator of the variance of the estimate of fixed effects used. In addition, the paper evaluates and compares the performance of the six approaches analytically, and some useful results are presented. Also, a simulation study for block designs was run to assess and compare the performance of the approaches based on their observed test levels. The simulation study shows that the approaches usually perform reasonably based on their test levels, and in some cases some approaches found to more adequately than other approaches. PubDate: Sat, 02 Mar 2024 01:30:21 +000

Abstract: This paper compares some Archimedean Copulas based on the range distribution and its application. We show that the Clayton Copula is better than the other Copula models considered in this paper. Also, Clayton Copula performed better than the regular one-way ANOVA when there were no outliers. However, when the data had outliers, the Clayton Copula performed almost at the same level (power-wise) as the regular one-way ANOVA.

Abstract: Markov chain Monte Carlo (MCMC) methods are a powerful and versatile tool with applications spanning a wide spectrum of fields, including Bayesian inference, computational biology, and physics. One of the key challenges in applying MCMC algorithms is to deal with estimation error. The main result in this article is a closed form, non-asymptotic solution for the sample error variance of a single MCMC estimate. Importantly, this result assumes that the state-space is finite and discrete. We demonstrate with examples how this result can help estimate and calibrate MCMC estimation error variance in the more general case, when the state-space is continuous and/or unbounded. PubDate: Thu, 29 Feb 2024 00:08:49 +000

Abstract: The present study investigates to what degree the common variance of the factor score predictor with the original factor, i.e., the determinacy coefficient or the validity of the factor score predictor, depends on the mean-difference between groups. When mean-differences between groups in the factor score predictor are eliminated by means of covariance analysis, regression, or group specific norms, this may reduce the covariance of the factor score predictor with the common factor. It is shown that in a one-factor model with the same group mean-difference on all observed variables, the common factor cannot be distinguished from a common factor representing the group mean-difference. It is also shown that for common factor loadings equal or larger than .60, the elimination of a d = .50 mean-difference between two groups in the factor score predictor leads to only small decreases of the determinacy coefficient. A compensation-factor k is proposed allowing for the estimation of the number of additional observed variables necessary to recover the size of the determinacy coefficient before elimination of a group mean-difference. It turns out that for factor loadings equal or larger than .60 only a few additional items are needed in order to recover the initial determinacy coefficient after the elimination of moderate or large group mean-differences. PubDate: Thu, 29 Feb 2024 00:01:49 +000