Journal of Probability and Statistical Science

Estimation of Population Size Using Ranked Set Sampling and Some of its Variations

Mohammad Fraiwan Al-Saleh, Lana Abdel Kareem Al-Ta'ani — Mon, 16 Oct 2023 00:00:00 -0600

The purpose of this paper is to estimate the population size of known total, using a sample that chosen using ranked set sampling technique and some of its variations; in particular, Ranked Set Sampling (RSS), Moving Extreme Ranked Set Sampling (MERSS) and Median Ranked Set(MRSS) are considered. The estimators obtained are compared with their counterparts using simple random sampling(SRS). It turned out that the estimators using RSS and its variations are more efficient than the corresponding estimators using SRS.

Recurrence Relations for Moment Generating Function Based on Progressive First Failure Censoring from Generalized Pareto Distribution and Characterization

Ali Sharawy — Mon, 16 Oct 2023 00:00:00 -0600

In this article, we establish recurrence relations (RR) for single and product moment generating function (MGF) based on based on progressive first failure censoring (PFFC) for generalized Pareto distribution (GPD). Characterization for GPD using RR of single and product MGF of PFFC are also obtained. Further, the results are specialized to the progressively type-II right censored (PTIIRCOS).

Generalized Estimator of Population Variance utilizing Auxiliary Information in Simple Random Sampling Scheme

Shiv Shankar Soni, Himanshu Pandey — Mon, 16 Oct 2023 00:00:00 -0600

In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.

New Series of Super-Saturated Design

Vaasanthi, Alugolu, Bhatracharyulu, N Ch — Mon, 16 Oct 2023 00:00:00 -0600

In this paper, a new series supersaturated design is proposed using Partially Balanced Incomplete Block Design through a combinatorial arrangement of the incidence matrix of a Balanced Incomplete Block Design. The method was illustrated with suitable example.

Keywords: SSD, incidence matrix, BIBD.

Transmuted Modified Weibull Distribution for Modeling Skewed Lifetime Dataset; Properties and Application

Awopeju Kabiru Abidemi, Alfred A. Abiodun — Mon, 16 Oct 2023 00:00:00 -0600

A new five parameter model called Generalized Modified Weibull distribution is proposed and studied. The new distribution generalizes the Modified Weibull Distribution introduced by Lai et al. (2003) using transformed – Transformer framework of Alzaatreh et al. (2014) which resulted to a distribution capable of modeling skewed data (positively or negatively skewed data), as well as, symmetric data. Property of a proper probability density function was used to ascertain that the resulting function is a proper probability density function. Statistical properties of the newly generated distribution were studied. Graph of probability density function of the distribution was used to show that it is capable of modeling skewed data. Graph of cumulative density functions of the distribution was plotted using varying parameter values. Monte Carlo simulation approach was used for the test of homogeneity of the distribution and it was observed that the parameters in the distribution approach the true values as sample size increases. Maximum likelihood Estimation method was used for estimation of the model parameters. Real life dataset was used for model comparison as well as demonstration of its application.

The Coefficient of Dependence and Conditioning

Stephen M. Scariano, Ananda B. W. Manage — Mon, 16 Oct 2023 00:00:00 -0600

The Coefficient of Dependence is introduced as an avenue for aiding student understanding of dependent, statistical events. The essential features of this coefficient are studied using different models and explored with multiple examples. Conditional probabilities are ultimately understood to be simple transformations of marginal probabilities via the Coefficient of Dependence, which is an idea well within the grasp of all undergraduate students. For completeness, proofs for the main results are relegated to the appendix for those interested.