This article introduces a novel transmuted half-logistic distribution by incorporating trigonometric functions into its transformation structure. The proposed distribution extends the classical half-logistic model, enhancing its effectiveness in capturing skewness and heavy-tail behaviour in data. We derive its statistical properties, moments, reliability measures and so on. Various parametric estimation procedures are employed to estimate the parameters, and simulation experiments are conducted to study their efficiency. In addition, the applicability of this model is demonstrated through real-world data analysis, showcasing its superiority over several established distributions based on various measures of criterion. AMS Subject Classification: 62E15, 62E10, 60E05
In recent years, the integration of data from multiple surveys has gained popularity in sample survey research. Broad-scale survey programmes often face practical challenges, including high survey data collection costs and increased demand for disaggregated statistics. These challenges were addressed through the integration of multiple survey data sets. Spatial parameters play a significant role in many surveys, leading to spatial non-stationarity, a phenomenon where the relationship between the study variable and covariates varies across locations. To address this issue and obtain more detailed information, sampling methodologies capable of efficiently handling spatial non-stationarity and integrating spatially referenced data are needed. This research introduced a Geographically Weighted Regression model-based Spatially Integrated estimator designed to estimate finite population totals by combining data from two separate surveys. The statistical characteristics of the proposed estimator were evaluated through an empirical design-based simulation study using real data from Crop Cutting Experiments and model-based spatial simulation studies, which demonstrated its superiority over traditional design-based estimators. Additionally, a spatial bootstrap method was developed to estimate the variance of the integrated estimator. AMS Subject Classification (2000): 62 D05
This article deals with the problem of testing the variances of two normal populations under the assumption that the mean parameters are equal. We propose an approximate likelihood ratio test and a test based on bootstrap observations. Two computational approach tests are suggested using the maximum likelihood estimators of the model parameters. Further, several generalized test methods are discussed to test the variances. Through a detailed Monte Carlo simulation study, the performances of the proposed test procedures are compared numerically in terms of their sizes and powers. Finally, we present real-life data sets to demonstrate the potential applicability of the suggested test procedures. AMS Subject Classification: 62F03, 62F05, 62F10, 65C05
One of the most important factors in determining a person’s demographic and economic standing in various migration regions is their movement, which is motivated by their professional prospects and socio-economic advancement. Aspiration is also a major factor in migration for an individual. However, a proper measure for this remains elusive. In this study, we aim to develop a new measure for mobility based on aspiration. Employment prospects, education and living standards are three elements that influence migration, according to individual socio-economic surveys. With the aid of these variables, we developed a model that captures the driving forces behind migration. Migration via aspiration: It is not always necessary to demonstrate upward mobility; occasionally, it is motivated by a person’s objectives, performance and long-term aspirations, which also vary depending on the situation and stage of life. This article focuses on methods for quantifying aspiration-based migration. To assess the distributional pattern of our suggested measure under different holding time distributions, we conducted a simulation study in this article. The practical component of the measure, which also focuses on the two different age groups, is examined by analyzing a real-life data set at the end of this study. To help policymakers address various regional issues and create new plans, this new aspirational migration measure provides a more realistic framework for the migration model. AMS Subject Classification: 60K15, 60J25, 62P25, 91D10
In the statistical literature, ‘effect size’ is typically defined as the estimate of a fixed or random effects in a linear or other statistical model. Here, a more explicit measure of the estimate of effect size is studied, defined generically as X ¯ / S , where X ¯ and S are the sample mean and sample standard deviation for a random sample of observations X 1 , X 2 , …, X n from a distribution with finite mean μ , variance σ 2 and finite moments of order 3 and 4, so that skewness and kurtosis are well defined (see section 2 for explicit formulae for the skewness and kurtosis for a univariate real valued random variable). For example, in a paired comparison experiment, the X i would be the differences between treatment and control measurements. The effect size has also been referred to in signal processing as the ‘signal-to-noise-ratio,’ and presents a measure of how easy it is to detect a signal ( μ ) in the presence of noise quantified by σ. The larger the effect size, the higher is the confidence that a signal is present. Accordingly, it is of interest to find interval estimates of the population effect size μ /σ. In this note, the asymptotic (normal) distribution of n ( X ¯ / S − μ / σ ) is determined, and an explicit variance-stabilizing transformation g is determined such that n ( g ( X ¯ / S ) − g ( μ / σ ) ) is asymptotically standard normal, making confidence intervals for the effect size relatively easy to compute numerically. This explicit formula for a variance stabilizing transformation for the effect size appears to be a new result in the mathematical statistics literature, and there is strong evidence that confidence intervals formed after applying a variance-stabilizing transformation have merit over central-limit-theorem-based confidence intervals. Therefore, for a random sample from any completely known univariate distribution, this result allows one to compute a relatively efficient confidence interval for the effect size. AMS Subject Classification: 62-01
