Estimating population parameters with a minimum error using survey data influenced by non-response is challenging. This has attracted the attention of researchers in this area of sampling. On the heels of the aforementioned problem, some classical estimators of the population mean utilizing the information on two auxiliary variables using a two-phase sampling scheme with sub-sampling of the non-respondents are proposed in this paper. Considered in this study is the case where the study and first auxiliary variables are affected by non-response while the supporting auxiliary variable is not affected by non-response. The expressions for the proposed estimators’ bias and mean square error have been derived up to the first order of approximation. Efficiency comparison of the proposed estimator with that of the usual estimator and some well-known existing estimators of the population mean have been carried out. The theoretical results have also been validated through some empirical investigations, and it is evident from the results that the proposed estimators will
be preferred in estimating population parameters from survey data with sensitive indicators that is inflicted with non-response.

KEYWORDS: Double sampling; sub-sampling; non-response; auxiliary variable.

Sustainable inventory management has become a key focus area for modern supply chains as organizations face increasing pressure to balance economic performance with environmental responsibility. One major challenge in this direction is the reduction of carbon emissions, which arise from activities such as production, transportation and warehousing. At the same time, trade credit has become an important financial mechanism through which suppliers allow buyers to delay payment for a specified credit period. Another critical factor affecting inventory cost is uncertainty in lead time demand. Variability in order processing, transportation delays and market fluctuations make lead time unpredictable. Modelling lead-time demand using an exponential probability distribution provides a realistic approach for minimizing stock out risk and determining an appropriate reorder level. This research develops a sustainable inventory model by jointly integrating carbon emission cost, trade credit policy and exponential lead time demand. The objective is to determine the optimal order quantity, reorder level their corresponding total cost and to analyse how changing parameters influences the overall system, thereby suggesting good managerial practices that lowers the total cost while balancing financial and environmental considerations.

KEYWORDS: Sustainable Inventory model; lead time demand; exponential distribution; trade credit; carbon emissions.

Count data arises frequently in every field of human activity, but regularly violate the equidispersion constraint imposed by the most popular distribution for analyzing these data, the Poisson distribution. The hyper-Poisson distribution, a generalization of the Poisson distribution is suitable for modeling count data having under dispersed, over dispersed and equi dispersed data sets. In this paper we consider a wide class of zero-inflated distributions as extended vesions of the zero-inflated Hermite distribution, the zero-inflated hyper-Poisson distribution and the zero-inflated modified hyper-Poisson distribution. We investigate several important properties of the distribution such as expressions for probability generating function, mean, variance, skewness, kurtosis etc. along with recursion formulae for probabilities, factorial moments and raw moments. The estimation of the parameters of the distribution is also attempted and it has been fitted to certain real life data sets for highlighting its practical relevance. Further, certain test procedures are applied for examining the significance of the parameters of the model and a simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the distribution.

KEYWORDS: confluent hypergeometric series; count data modeling; generalized likelihood ratio test; Rao’s efficient score test; simulation.

Cumulative Sum Control Charts (CSCC) is used to maintain current control by continuous inspection of a manufacturing process. Khaparde and Dhabe (2010) developed the Control Charts For Random Queue Length N for (M/M/1) : (?/FCFS) Queuing Model. Therefore, in this paper, CSCC has been developed for Marshall-Olkin Extended Exponential (MOEE) Distribution considering quality High way Road Construction with application of Queuing Theory. These charts are useful where quality characteristics are measured by product life time. The expression for Average Run Length (ARL) has been derived. Numerical examples have been included to illustrate the mathematical findings. Some martingales related to cumulative sum tests and single-server queue has been discussed.

KEYWORDS: CSCC; Marshall-Olkin Extended Distribution; Queuing Theory; ARL.

In this paper, we estimate the location parameter (?) and scale parameter (?) of a distribution symmetric about ? using U-statistics with kernels as the BLUE’s of ? and ? based on systematic statistics, viz., quasi-midrange and quasi-range of the sample. We also provide explicit expressions for the variance of these U-statistics. The advantage of the estimators obtained in this paper is that the order of the covariance matrix involved in expressions for the variance of the U-statistics is less, thus making the computation of the variance of U-statistics much easier.

KEYWORDS: best linear unbiased estimators; location and scale parameters; quasi-midrange; quasi-range; U-statistics.