Paired double-ranked set sampling

Efficient class of ratio cum median estimators for estimating the population median

In estimation theory, the use of auxiliary information significantly improves precision while estimating population parameters. In this paper, an efficient class of ratio cum median estimators of the population median is suggested using simple random sampling without replacement. The expressions for bias and mean square error of the proposed class are derived theoretically. The condition for the asymptotic optimum estimator is obtained with its bias and mean square error expressions. Under certain realistic conditions, the asymptotic optimum estimator is more proficient, based on analytical and numerical comparisons with some existing estimators that are members of the suggested class of estimators. The superiority of the proposed ratio cum median estimators is shown through real data applications. Such a new proposed estimator will be useful in the future for data analysis and making decisions.

A SkSP-R Plan under the Assumption of Gompertz Distribution

In this study, we designed a time-truncated SkSP-R sampling plan when the lifetime of units follows a Gompertz distribution (GmzD). The GmzD is briefly discussed. All of the plan parameters were obtained using a two-point approach, which is based on limiting quality level (LQL) and acceptable quality level (AQL). Moreover, operating characteristic (OC) values were calculated for the determined value of the plan parameters by using the OC function of the SkSP-R. Applications of two real life situations in engineering were presented to illustrate the applicability of the offered sampling inspection plan. It was found that the new SkSP-R sampling inspection plan can be used efficiently in the field.

A Two-Parameter Model: Properties and Estimation under Ranked Sampling

This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions.