Open Access Original Research Article

Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

Rauf Ibrahim Rauf, Okoli Juliana Ifeyinwa, Haruna Umar Yahaya

Asian Journal of Probability and Statistics, Page 1-17
DOI: 10.9734/ajpas/2021/v15i230348

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.

Open Access Original Research Article

The Equilibrium Renewal Burr XII Distribution: Properties and Applications

Abdulzeid Yen Anafo, Lewis Brew, Suleman Nasiru

Asian Journal of Probability and Statistics, Page 18-40
DOI: 10.9734/ajpas/2021/v15i230349

In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.

Open Access Original Research Article

Calibration Approach Product Type Estimators of Population Mean in Stratified Sampling with Single Constraint: A Comparison of Three Distance Measures

Enang, Ekaette Inyang, Ojua, Doris Nkan, T. T. Ojewale

Asian Journal of Probability and Statistics, Page 41-58
DOI: 10.9734/ajpas/2021/v15i230350

This study employed the method of calibration on product type estimator to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure for single constraint. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators was carried out using real life and stimulated data set. The result with the real life data showed that the proposed calibration product type estimator  produced better estimates of the population mean  compared to   and . Results from the simulation study showed that the proposed calibration product type estimators had a high gain in efficiency as compared to the product type estimator. The simulation result also showed that the proposed estimators were more consistent and reliable under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better if the underlying distributional assumption is normal in nature.

Open Access Original Research Article

Exponential-Ratio-Type Imputation Class of Estimators using Nonconventional Robust Measures of Dispersions

Ahmed Audu, Mojeed Abiodun Yunusa, Aminu Bello Zoramawa, Samaila Buda, Ran Vijay Kumar Singh

Asian Journal of Probability and Statistics, Page 59-74
DOI: 10.9734/ajpas/2021/v15i230351

Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known auxiliary variable parameters that can be influenced by outliers. In this paper, we suggested new classes of exponential-ratio-type imputation method that uses parameters that are robust against outliers. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.

Open Access Original Research Article

A New Two-Parametric Maxwell-Rayleigh Distribution: Application to the Analysis of Engineering Data

Muzamil Jallal, Aijaz Ahmad, Rajnee Tripathi

Asian Journal of Probability and Statistics, Page 75-89
DOI: 10.9734/ajpas/2021/v15i230352

In this study a new generalisation of Rayleigh Distribution has been studied and referred it is as “A New Two-Parametric Maxwell-Rayleigh Distribution”. This distribution is obtained by adopting T-X family procedure. Several distributional properties of the formulated distribution including moments, moment generating function, Characteristics function and incomplete moments have been discussed. The expressions for ageing properties have been derived and discussed explicitly. The behaviour of the pdf and Hazard rate function has been illustrated through different graphs. The parameters are estimated through the technique of MLE. Eventually the versatility and the efficacy of the formulated distribution have been examined through real life data sets related to engineering science.