A Note On Beta Inverse-Weibull Distribution

The inverse Weibull distribution is one of the widely applied distribution for problems in reliability theory. In this article, we introduce a generalization—referred to as the Beta Inverse-Weibull distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of the Beta Inverse-Weibull distribution. The shapes of the corresponding probability density function and the hazard rate function have been obtained and graphical illustrations have been given. The distribution is found to be unimodal. Results for the non central moments are obtained. The relationship between the parameters and the mean, variance, skewness, and kurtosis are provided. The method of maximum likelihood is proposed for estimating the model parameters. We hope that this generalization will attract wider applicability to the problems in reliability theory and mechanical engineering.     

Optimal designing of skip-lot sampling plan of type SkSP-2 with group acceptance sampling plan as reference plan under Burr-type XII distribution

In this paper, skip-lot sampling plan of type SkSP-2 with group acceptance sampling plans is proposed when the lifetime of the product follows the Burr-type XII distributions. The optimal parameters of the proposed plan are determined when two points on operating characteristics curve namely acceptable quality level and limiting quality level and the number of testers are specified. We also considered the Burr-type XII distribution to find the plan parameters. Several tables are given for practical use. We compare the results of proposed plan with the existing plans. Results are explained using real-world examples.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

Bayesian analysis of the amended Davidson model for paired comparison using noninformative and informative priors

In recent years, numerous statisticians have focused their attention on the Bayesian analysis of different paired comparison models. While studying paired comparison techniques, the Davidson model is considered to be one of the famous paired comparison models in the available literature. In this article, we have introduced an amendment in the Davidson model which has been commenced to accommodate the option of not distinguishing the effects of two treatments when they are compared pairwise. Having made this amendment, the Bayesian analysis of the Amended Davidson model is performed using the noninformative (uniform and Jeffreys’) and informative (Dirichlet–gamma–gamma) priors. To study the model and to perform the Bayesian analysis with the help of an example, we have obtained the joint and marginal posterior distributions of the parameters, their posterior estimates, graphical presentations of the marginal densities, preference and predictive probabilities and the posterior probabilities to compare the treatment parameters.     

Bayesian inference of the inverse Weibull mixture distribution using type-I censoring

A large number of models have been derived from the two-parameter Weibull distribution including the inverse Weibull (IW) model which is found suitable for modeling the complex failure data set. In this paper, we present the Bayesian inference for the mixture of two IW models. For this purpose, the Bayes estimates of the parameters of the mixture model along with their posterior risks using informative as well as the non-informative prior are obtained. These estimates have been attained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. For the former case, Bayes estimates are obtained under three loss functions while for the latter case only the squared error loss function is used. Simulation study is carried out in order to explore numerical aspects of the proposed Bayes estimators. A real-life data set is also presented for both cases, and parameters obtained under case when shape parameter is known are tested through testing of hypothesis procedure.     

Double-sampling regression-cum-exponential estimator of the mean of a sensitive variable

ABSTRACT

A flexible scrambled response model using a randomization device for quantitative sensitive data is used to evaluate the protection of respondents’ privacy. A double-sampling regression-cum-exponential estimator is used to estimate the mean of a sensitive variable using the mean of a nonsensitive auxiliary variable under scrambled response. The expected bias, the expected mean square error, and the minimum mean square error of this exponential-type estimator are expressed. Simulations and empirical results show that the proposed estimator under scrambled response model has a lower mean square error and a lower bias than the ratio and the exponential estimators.     

Description and Propagation of Uncertainty in Input Parameters in Environmental Fate Models

Today, chemical risk and safety assessments rely heavily on the estimation of environmental fate by models. The key compound‐related properties in such models describe partitioning and reactivity. Uncertainty in determining these properties can be separated into random and systematic (incompleteness) components, requiring different types of representation. Here, we evaluate two approaches that are suitable to treat also systematic errors, fuzzy arithmetic, and probability bounds analysis. When a best estimate (mode) and a range can be computed for an input parameter, then it is possible to characterize the uncertainty with a triangular fuzzy number (possibility distribution) or a corresponding probability box bound by two uniform distributions. We use a five‐compartment Level I fugacity model and reported empirical data from the literature for three well‐known environmental pollutants (benzene, pyrene, and DDT) as illustrative cases for this evaluation. Propagation of uncertainty by discrete probability calculus or interval arithmetic can be done at a low computational cost and gives maximum flexibility in applying different approaches. Our evaluation suggests that the difference between fuzzy arithmetic and probability bounds analysis is small, at least for this specific case. The fuzzy arithmetic approach can, however, be regarded as less conservative than probability bounds analysis if the assumption of independence is removed. Both approaches are sensitive to repeated parameters that may inflate the uncertainty estimate. Uncertainty described by probability boxes was therefore also propagated through the model by Monte Carlo simulation to show how this problem can be avoided.     

Repercussions of exchange rate depreciation on the economy of Pakistan: Simulation analysis using macroeconometric model

Expansionary and contractionary effects of exchange rate shock in developing economies has been the subject of an extensive debate but the results are inconclusive. This study has been conducted to examine the repercussions of unexpected exchange rate depreciation in the Pakistan economy. Unlike the previous literature, this study utilizes a fairly large macroeconometric model constructed on the basis of Cowles Commission structural approach. The study explores that expansionary effect of exchange rate depreciation explained by the traditional theories of open economy macroeconomics persists only for one fiscal year but these theories don’t work in the long-run as contractionary phase starts in the subsequent years. Monetary and fiscal authorities are not neutral and contractionary policy is taken in response to depreciation which pushes the economy into recession. Stagflationary effects are clearly observed. However, improvement in foreign sector prolongs for a number of years and policy makers would have to face a trade-off between opposite response of output and current account balance. Hence, unexpected depreciation generates sharp cyclical fluctuations on demand which immediately transmit to supply side of the economy. In line with the views of “New Structuralists”, exchange rate depreciation may be considered as a source of shock rather than shock absorber in the case of Pakistan economy. Although this study is specifically estimated for the Pakistan economy, authors believe that their methodological contributions and results are of wider importance for policy makers in developing countries.     

Psychological Assessment through Performance-Based Techniques and Self-Reports: A Case Study of a Sexually Abused Girl at Preschool Age

We investigated the implicit psychological and behavioral consequences of sexual abuse in an adolescent girl who suffered child sexual abuse at preschool age in this case report. We report the manifestations of this abuse on her personality and psychological functioning using a structured clinical interview and a comprehensive psychological battery including the Beck Anxiety Inventory, the Beck Depression Inventory, the Standard Progressive Matrices, Rorschach Ink Blots, and the Schema Mode Inventory. These investigations were useful in formulating both a diagnosis and a management plan. The girl fulfilled diagnostic criteria for a major depressive episode and borderline personality disorder. This combination of psychological testing may be useful in establishing an accurate multiaxial diagnosis and for understanding the behavioral and psychological sequelae of child sexual abuse in similar cases. The study further suggests that schema-focused therapy is a useful therapeutic tool for individuals who have suffered child sexual abuse at an early age and who have borderline personality disorder.     

Secular–religious debates on the Indonesian National Education System: colonial legacy and a search for national identity in education

This paper attempts to trace and discuss the historical roots of secular–religious debates and tensions and their relationship to the formation of the Indonesian National Education System within the context of the history of Dutch colonization and nationalist struggles for national identity. It focuses on what are believed to be two ‘significant events’ in the history of the Indonesian National Education System. The first is three and half centuries of Dutch occupation of Indonesia prior to 1945 and the second the establishment of the Indonesian National Education System. Also, the tension between those desiring a secular versus religious (Islamic) education system is discussed in detail.