In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the efficiency conditions. Besides theoretical efficiency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

Aim: To find out how accurate the Alvarado and Tzanaki scoring systems are in diagnosing acute appendicitis taking histopathology as gold standard. Methods: A cross-sectional prospective study was conducted from August 2019 to July 2020 at Department of General Surgery, Pakistan Institute of Medical Sciences Islamabad. Sixty patients were included, all of whom had appendectomies after a clinical diagnosis of acute appendicitis. Samples were submitted for histopathology, which was used as the gold standard for the definitive diagnosis of acute appendicitis. The specificity, sensitivity, positive predictive value (PPV), negative predictive value (NPV), diagnostic accuracy and negative appendectomy rate of Alvarado and Tzanaki scoring systems was calculated using SPSS version 23. Results: The sensitivity, specificity, positive predictive value, negative predictive value and diagnostic accuracy of Alvarado score at optimal cut-off threshold of ≥7.0, were calculated as 74%, 55%, 90%, 27% and 71.66% respectively. The cut-off threshold point of Tzanaki score was set at more than 8, which yielded a 94.11% sensitivity and an 88.88% specificity. The positive predictive value was 99.95% and the negative predictive value was 72.72%. The Alvarado and Tzanaki scoring systems had negative appendectomy rates of 9.5% and 2.04%, respectively. Conclusion: The Tzanaki scoring system has a better diagnostic accuracy for acute appendicitis as compared to the Alvarado score. Keywords: Acute appendicitis, Alvarado score, Tzanaki score

Extensive pumping and less recharge of groundwater increase concentration of Arsenicin it; thus, make it injurious for human health. This study explores the water quality indicators of groundwater of the arid and populous areas of Southern Punjab – Pakistan, which experiences extensive pumping for irrigation and drinking purposes. Spatial data of 550 locations from the three major cities of this area namely Multan, Muzaffargarh, and Khanewal were collected to observe the 8 well known water quality indicators set by Pakistan Environmental Protection Agency (PEPA) and World Health Organization (WHO). Firstly, we computed pairwise correlation coefficients among these indicators and later on contamination load for this data was also calculated by using factor analysis. Several regression models were fitted and the established equations were evaluated based on their coefficient of determination for pairs of variables. Factor analysis suggested 3 groups of indicators that were chemically correlated and showed concurrence with regression analysis. Among the water samples, 27% showed undesired Arsenic concentration that violated thePEPA and WHO standards. Lastly, we spatially mapped these indicators to predict the unmonitored locations which will enable stakeholders and policymakers to take decisions in the best interest of the health of community living in these areas.

In this paper, we propose a generalized class of exponential-type estimators for estimating the finite population distribution function using dual auxiliary variables under stratified sampling. The biases and mean squared errors (MSEs) of the proposed class of estimators are derived up to the first order of approximation. The empirical and theoretical study of comparisons is discussed. Four populations are taken for the support of the theoretical findings. It is observed that the proposed class of estimators performs better as compared to all other considered estimators in stratified sampling.

This article fundamentally aims at the proposition of new family of estimators using auxiliary information to assist the estimation of finite population mean of the study variable. The objectives are achieved by devising dual use of supplementary information through straightforward manner. The additional information is injected in mean estimating procedure by considering squared values of auxiliary variable. The utility of the proposed scheme is substantiated by providing rigorous comparative account of the newly materialized structure with the well celebrated existing family of Grover and Kaur (2014). The contemporary advents of the new family are documented throughout the article.