Calcutta Statistical Association Bulletin

The Laplace distribution is popular in the fields of economics and finance; however, empirical data often exhibit asymmetry and boundedness on one side of the support, features that the Laplace distribution fails to capture. To address this limitation, we propose a new family of skewed distributions using the skewing mechanism of Azzalini^[1], namely, the skew-symmetric-Laplace-uniform distribution (SSLUD). In this formulation, the uniform distribution serves a dual role by introducing skewness into the Laplace distribution and simultaneously restricting the distribution’s support to one side of the real line. This article provides a comprehensive description of the essential distributional properties of SSLUD. Estimators of the parameter are obtained using the method of moments under the permissible range of the parameter and the method of maximum likelihood. The finite sample and asymptotic properties of these estimators are studied using simulation. It is observed that the maximum likelihood estimator performs better than the constrained moment estimator, as demonstrated through a simulation study. Finally, the practical applicability of the proposed model is illustrated using real-world data comprising 348 automobile bodily injury log-claim amounts, and its performance is compared with that of standard competing distributions.

AMS Subject Classification: 62E10, 62F10

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 X₁, X₂, …, X_n from a distribution with finite mean μ, variance σ² 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

This article proposes two estimators for two semiparametric count regression models, namely semiparametric partially Poisson (SPPO) and semiparametric partially zero-inflated Poisson (SPZIP), via the penalized smoothing (Ps) spline and P-spline (Pb) estimations to address the common issue of nonparametric relationships between the response variable and covariates. Additionally, the SPZIP model incorporates a zero-inflation component to handle excess zeros in count data. Through extensive Monte Carlo simulations, we rigorously evaluate the performance of the proposed penalized spline estimators by comparing them against traditional parametric estimators using multiple statistical criteria, including the Akaike information criterion, Bayesian information criterion, deviance statistic, mean squared error and root mean squared error (RMSE). The results indicate that our estimators are more efficient than other estimators. Also, the SPZIP and SPPO models consistently outperform parametric (Poisson and zero-inflated Poisson) regression models, particularly in scenarios with high levels of zero inflation, demonstrating their superior ability to model complex data structures. Our findings highlight the practical utility of these models for analyzing complex count data with excess zeros and nonparametric covariate effects. A real-life data application further demonstrates the capabilities of the SPPO and SPZIP models, demonstrating their ability to provide more accurate and adaptable statistical analysis in challenging data settings.

AMS Subject Classification: 62G08, 62J20, 62J05

Panel count data arise when recurrent events experienced by the study subjects are recorded only at discrete observation times. In this article, we focus on the regression analysis of panel count data with multiple modes of recurrence. We introduce a proportional mean model to assess the effects of covariates on the underlying counting processes corresponding to different recurrence modes. The methodology includes the joint estimation of baseline cumulative cause-specific mean functions and regression coefficients. We also establish the asymptotic properties of the proposed estimators. A Monte Carlo simulation study is conducted to examine the performance of the proposed estimators in finite samples. We illustrate the practical applicability of the procedures using two real-life data sets.

AMS Subject Classification: 62P10

This article considers a classical optimal design problem of finding saturated D-optimal designs for the quartic polynomial model for mixture experiments. The necessary and sufficient conditions of the optimality criterion are confirmed by using the corresponding equivalence theorem.

AMS Subject Classification: 62K05

When a sufficiently strong correlation exists between the study variable Y and the auxiliary variable X , the ranks of the auxiliary variable R x are also correlated with the values of the study variable Y . As a result, these ranks can enhance the precision of the estimators. In this article, we propose a general class of difference-cum-ratio-type exponential estimators for the finite population mean under the stratified random sampling scheme, utilizing both the auxiliary variable X and its rank R x . Up to first-order of approximation, we derive the mathematical expressions for the bias and mean squared error (MSE) of the proposed estimator, as well as for other existing estimators. We apply the proposed method to two real data sets, and a simulation study is carried out using an artificially generated bivariate population to observe the performance of the estimators. The results indicate that the proposed estimator consistently yields a lower MSE and higher relative efficiency compared to other existing estimators. The numerical evidence demonstrates that the proposed estimator outperforms all other existing alternatives in various scenarios. We conclude that the general class of estimators presented in this study exhibits superior performance compared to all other existing estimators.

AMS Subject Classification: MSC2020, 62D05

In this article, we have proposed a difference-cum-exponential type estimator for estimating population mean by using information on two auxiliary variables under non-response, in which the expressions of bias and mean square error of the proposed estimator have been derived up to the first order of approximation. The suggested estimator has been compared with other existing and adaptive estimators theoretically and empirically. Also, a simulation study has been performed; for this, we have generated two artificial data sets to demonstrate the efficiency of the proposed estimator than the other estimators.

AMS Subject Classification: MSC2020, 62D05