##### An Inventory Model with Three Parameter Weibull Distribution for Deteriorating Items under Inflation

Akaninyene Udo Udom, Pascal Nnamdi Odoh

Asian Journal of Probability and Statistics, Page 1-17
DOI: 10.9734/ajpas/2022/v18i230438

This study explores a predetermined inventory system for deteriorating items with a Weibull distribution, taking into consideration nonlinear demand and trade credit under inflation and allowing for shortages and partial backlogs. The reason for this study is to find the appropriate order and replenishment policy to actually reduce relevant costs. The model is built under two scenarios; case  1: $$\left(0 \leq M \leq t_{2}\right)$$ . The consumer will be charged interest on the outstanding debt if he does not pay the provider by time M. and case 2:  $$\left(0 \leq t_{1} \leq M\right)$$  if the consumer gets to sell all of his commodity as well as earns interest on the revenue until the account is settled. To demonstrate the use and performance of the model, numerical approach and sensitivity analysis are actually given. As a result, this model will assist retailer in determining the optimal replenishment cycles in a variety of situations, as well as provide an innovative management insight that will aid the industry reduce relevant cost.

##### Respiratory Syncytial Virus Infection in Infants: A Comparative Study Using Discriminant, Probit and Logistic Regression Analysis

Orumie, Ukamaka Cynthia, Desmond Chekwube Bartholomew

Asian Journal of Probability and Statistics, Page 18-31
DOI: 10.9734/ajpas/2022/v18i230440

In babies, respiratory syncytial virus (RSV) is the most common cause of lung inflammation (pneumonia) or bronchiolitis (inflammation of the lungs' airways). This virus comes with several symptoms such as congested or runny nose, dry cough, low-grade fever, sore throat, sneezing, headache, difficulty in breathing etc. The virus can cause death in babies if not properly managed and therefore calls for immediate investigations to reveal the significant causes. Several research works have been conducted but the idea of investigating more potential predictor variables and the application of both regression and classification models have been grossly understudied. Therefore, unpublished secondary data collected from three different hospitals in Port Harcourt, Rivers State, Nigeria on fifteen predictor variables which are potential causes of RSV are modeled using two categorical regression approaches – logistic and probit regression models and one classification model – discriminant function analysis. The models were compared using misclassification errors, Receiver Operating Characteristic (ROC) plot, concordance, sensitivity, specificity and pseudo R-square values. The linear discriminant function model outperformed both the logit and probit models. The results showed that paternal history of asthma, maternal history of asthma, mother’s occupation, mother’s smoking habit and mother’s education level were the most important variables to linearly classify seropositive and seronegative RSV patients.

##### Mangat Randomized Response Group Testing Theory

Asian Journal of Probability and Statistics, Page 32-40
DOI: 10.9734/ajpas/2022/v18i230442

This paper proposed a new Randomized Response Group Testing (RRGT) model that estimates proportion of people characterizing a sensitive variable under study. Simple random sampling with replacement, binomial probability distribution and maximum likelihood were used as randomization procedure, sampling model and estimation technique, respectively. The distributional properties (expectation and variance) of the proposed estimator, efficiency comparison of the model with some existing models, and numerical illustration of all the competing models were also explored. The study found that the developed model outperformed competing existing orthodox RRMs and earlier RRGT model in terms of efficiency, privacy protection and it is economically advantageous.

##### Perfect i.i.d Processes

Pathikrit Basu

Asian Journal of Probability and Statistics, Page 41-45
DOI: 10.9734/ajpas/2022/v18i230443

This note proves a theorem about i.i.d. i.e. independent and indentically distributed processes, when the index space is a measure space. The statement of the problem corresponding to the theorem proved in this paper appears in [1], in which the concept of a sample distribution limit corresponds to the concept of a perfect i.i.d process in this paper.
Theorems proved in this theme, regarding existing and non-existence, have been shown in the economics literature, when the index set is [0; 1], in [2], [3], [4], [5]. The approach taken in this
paper is perhaps, surprisingly elementary. We may apply standard measure extension theorems to show existence. These may be found in [6], [7].

##### Impact of Maternal Education and Age on Weight of Child at Birth: Use of Multinomial Logistic Model

D. C. Bartholomew, O. E. Biu, D. Enegesele

Asian Journal of Probability and Statistics, Page 46-59
DOI: 10.9734/ajpas/2022/v18i230444

The World Health Organization (WHO) prescribed 2.5 kilograms to 4.2 kilograms as the standard for normal birth weight (NBW) and every child whose birth weight is below the lowest bound is regarded as low birth weight (LBW) while above the highest bound is regarded as macrosomia. The odds for a LBW child to die as reported is about 40 times high when compared to a NBW child and these overwhelming death records are higher in developing countries. Therefore, urgent research about the causes of LBW especially in developing countries is very necessary and this motivated this research in Nigeria. In this paper, the Multinomial Logistic Regression (MLR) model was applied to secondary data from the 2018 Nigerian Demographic and Health Survey (NDHS) report to predict the probability of giving birth to NBW and macrosomia babies referenced to LBW babies. The maternal education level and age were considered as the predictor variables. The data was naturally stratified by maternal education level, that is (1 = Higher Education, 2 = Secondary Education, 3 = Primary Education, and 4 = No Education). The equal sample allocation technique which assigns equal stratum sample sizes (ni =  200 for the ith maternal education level) was adopted. The 800 sample size was reduced to 735 after screening for outliers in the maternal age variable. Considering the 54 LBW babies, 57% (0.5741) were from mothers with no education. The results showed that maternal education level and age have causal effects on child birth weight in Nigeria. Younger mothers (less than 28years) are 96.5% likely to have LBW babies while mothers who attained a minimum of primary, secondary, and higher education are 88.00%, 82.00%, and 57.90% likely to have NBW babies respectively when compared to those with no formal education. The research recommends that mothers should acquire at least primary school education and early child marriage (less than 28years) of the girl child should be discouraged.