All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

Background: Breastfeeding has the most profound impact on infant health and wellness, and also have significant implications for the mother. The duration of the breastfeeding determines the infant’s protection from malnutrition and other common infectious diseases; consequently, the World Health Organization (WHO) recommends exclusive breastfeeding (EBF) six months, followed by gradual weaning and breastfeeding until the baby is two years old. In Pakistan, the practice of breastfeeding is heavily dependent upon certain demographic, economic, social, and biological factors, which ultimately impact the quality of care provided to the infant and their health. The aim of this paper, therefore, is to measure the impact of these factors on the exclusive breastfeeding duration in Pakistan. Methods: The data for the study has been collected from Pakistan Demographic and Health Survey (PDHS) for the year 2017–18. Binary logistic regression model and survival analysis are used to determine the relationship between the independent and dependent variables. Results: We use a binary logistic regression to estimate the effect of each factor on the duration of EBF. The binary logistic regression finds significant relationships between region, maternal education, wealth index, size of a child, watching television, delivery by cesarean, and maternal age and EBF. We then use log-likelihood, AIC, BIC criteria to determine if a parametric or non-parametric model would provide a better fit; based on these results we fit an Inverse Gaussian (Weibull) distribution for the survival analysis. These results show that there are more significant factors associated with EBF duration in parametric survival analysis than in the binary logistic regression results. Thus, the survival analysis is a better method for predicting the relationship between the duration of EBF and its factors. Furthermore, logically EBF is designated to be done for six months which would not be properly gauged with a binary response variable. Conclusions: The results of this study provide proof that exclusive breastfeeding is a common practice among women in Pakistan, and to improve the quality of post-natal care, health policy in the country needs to focus on the existing demographic and social factors which are found significant in this study.

In this paper we have suggested an improved class of ratio type estimators in estimating the finite population mean when information on minimum and maximum values of the auxiliary variable is known. The properties of the suggested class of estimators in terms of bias and mean square error are obtained up to first order of approximation. Two data sets are used for efficiency comparisons.

The 2019 coronavirus disease (COVID-19), caused by the SARS-CoV-2 virus has affected the social determinants of health, worsening health inequities and deteriorating healthcare capacities around the globe. The objective of this study is to investigate the COVID-19 prevention behaviors within the framework of the Health Belief Model in the city of Depalpur in the Okara District of Pakistan in May 2020. Using an observational, cross-sectional, and quantitative study design, a face-to-face field survey was conducted during the epidemic of COVID-19 in district Okara, Pakistan. A sample of 500 adults was selected from the city of Depalpur the in Okara district of Pakistan, using a two-stage sampling design with cluster sampling in stage one and systematic random sampling at stage two. A COVID-19 prevention behavior scale was computed based on twelve dichotomous items. Descriptive statistics, analysis of variance (ANOVA), and negative binomial regression analyses were performed. The most common prevention behavior among study participants was avoiding going for walks in the parks (81.0%), followed by not leaving home during the lockdown (72.6%), and washing hands every day with soap and water for 20 s after going out of their home (64.0%). Fewer people exhibited prevention behaviors such as social distancing (e.g., staying at least six feet away from other people) which in the EU was recommended to be a minimum of 1.5–2 m (44.4%) and following all of the basic protective measures (e.g., hand washing, use of a face covering in public, social distancing) in order to protect against COVID-19 (33.0%). The results from the negative binomial regression analysis showed that after controlling for the other HBM constructs and sociodemographic factors, only the perceived benefits of preventative actions showed significant association with the prevention behavior scale (IRR, 1.16; CI, 1.061–1.276; p < 0.001). The study findings show that public health interventions attempting to control the spread of COVID-19 in Pakistan may want to affect a change in people’s perceived benefits of preventative actions through mass awareness-raising campaigns.

Background: Underweight prevalence continues to be major public health challenge worldwide, particularly in developing countries like Pakistan. This study is focused on socio-economic and demographic aspects of underweight prevalence among children under-five in Punjab. Methods: In this study, several socioeconomic and demographic factors are considered using MICS-4 data-set. Only those variables which are usually described in the nutritional studies of children were picked. Covariates include: the age of children, sex of the children, age of mother, total number of children born to women, family wealth index quintile, source of drinking water, type of sanitation, place of residence, parents’ education and occupation. All Categorical variables are effect coded. The child’s age and the mother’s age are assumed to be nonlinear, geographical region is spatial effect, while other variables are parametric in nature. Since, the response is binary, covariate comprises linear terms, nonlinear effects of continues covariates and geographic effects, so we have use Geo-additive models (based on Fully Bayesian approach) with binomial family under logit link. Statistical analysis is performed on Statistical package R using Bayes X and R2 Bayes X Libraries. Results: Underweight status of children was found to be positively associated with number of under-five children in household, total number of children ever born to women and age of mother when the child was born. Whereas, it negatively associated with place of residence, parent’s education and family wealth index quintile. On the regional effect, the Southern Punjab has higher prevalence of underweight compared to Central and Northern Punjab. Conclusion: Similarity of our results with several other studies demonstrate that the Geo-additive models are an ideal substitute of other statistical models to analyze the underweight prevalence among children. Moreover, our findings suggest the Punjab Government, to introduce target-oriented programs such as poverty reduction and enhancement of education and health facilities for poor population and disadvantaged regions, especially Southern Punjab.

This study proposes EWMA-type control charts by considering some auxiliary information. The ratio estimation technique for the mean with ranked set sampling design is used in designing the control structure of the proposed charts. We have developed EWMA control charts using two exponential ratio-type estimators based on ranked set sampling for the process mean to obtain specific ARLs, being suitable when small process shifts are of interest.