Bivariate Setup Research Articles

Bivariate Extension of Weighted Dynamic Survival Extropy and Its Quantile Approach

This paper considers shift-dependent survival extropy in a bivariate setup and studies its properties. We also look into the problem of extending the same measure for conditionally specified models. It is shown that the proposed measure uniquely determines the distribution. Also, we established nonparametric estimators for the conditionally specified model, and the asymptotic properties of the proposed estimator are established under some regularity conditions. The effect of the proposed estimator is illustrated using simulated and real data sets. We have also proposed a quantile-based measure which uniquely determines the distribution. Also, we have obtained the real-life application of the proposed measure for a quantile function whose distribution function does not exist.

Extended fractional cumulative past and paired [formula omitted]-entropy measures

Very recently, extended fractional cumulative residual entropy (EFCRE) has been proposed by Foroghi et al., (2022). In this paper, we introduce extended fractional cumulative past entropy (EFCPE), which is a dual of the EFCRE. The newly proposed measure depends on the logarithm of fractional order and the cumulative distribution function (CDF). Various properties of the EFCPE have been explored. This measure has been extended to the bivariate setup. Furthermore, the conditional EFCPE is studied and some of its properties are provided. The EFCPE for inactivity time has been proposed. In addition, the extended fractional cumulative paired ϕ-entropy has been introduced and studied. The proposed EFCPE has been estimated using empirical CDF. Furthermore, the EFCPE is studied for coherent systems. A validation of the proposed measure is provided using logistic map. Finally, an application is reported.

Statistical inference for tail-based cumulative residual entropy

Tail risk analysis plays a central strategic role in risk management, and focuses on the problem of risk measurement in the tail regions of extreme risks. In this paper, by extending the entropy method, we propose a quantity called Tail-based Cumulative Residual Entropy (TCRE) in a bivariate set-up as an alternative measurement of qualifying tail risk variability, which is less addressed in the literature. The TCRE in a bivariate set-up can be viewed as the tail cumulative residual entropy for a random vector (X,Y) with some dependence structure, and the combination of it with the Marginal Expected Shortfall (MES) constitutes a new risk measure called Marginal CRE Shortfall (MCRES). For a wide class of bivariate extreme value distributions, we construct a nonparametric estimator of the proposed TCRE measure and establish an asymptotic distribution of the estimator with extreme high-level tail. We use extreme value techniques to calculate the limit of the proposed measure as the risk level approaches to the extreme status and present how the tail dependence structure and marginal risk severity have an influence on its limits. Furthermore, a simulation study and real data analysis of the proposed TCRE are presented to understand and verify the properties of TCRE and its estimators.

FACTORS CONTRIBUTING TO ADOPTION OF AGRICULTURAL TECHNOLOGIES: A CASE OF INTEGRATED PEST MANAGEMENT (IPM) IN KHULNA DISTRICT OF BANGLADESH

This study tries to find the contributing factors of the Integrated Pest Management (IPM) adoption behavior of Bangladeshi farmers. For analysis, the necessary information was collected from 345 farmers residing in Phultala Upazila of Khulna division, Bangladesh with structured questionnaires. A simple random sampling technique was applied for data collection. In the bivariate setup, the association between the adoption status of IPM and possible contributing factors was examined by performing a chi-square test. A multivariable logistic regression was applied in a multivariate setup. The estimates of the model provide evidence that farmers’ education level, farm size, training status on IPM, membership status of IPM club and farmer’s field school have significant effects on farmers’ adoption behavior of IPM. The findings call for greater attention on the part of the government for increasing farmers’ education level, facilitating more training programs and arranging several motivational seminars on IPM at the primary level.

Prevalence of Diabetes Mellitus and Its Associated Factors in Bangladesh: Application of Two-level Logistic Regression Model

This study intends to explore the prevalence of diabetes mellitus (DM) and its associated factors in Bangladesh. The necessary information was extracted from Bangladesh Demographic and Health Survey (BDHS) 2011. In bivariate analysis, Chi-square test was performed to assess the association between selected covariates and diabetes status. A two-level logistic regression model with a random intercept at each of the individual and regional level was considered to identify the risk factors of DM. A total of 7,535 individuals were included in this study. From the univariate analysis, the prevalence of DM was found to be 33.3% in 50–54 age group for instance. In bivariate setup, all the selected covariates except sex of the participants were found significant for DM (p < 0.05). According to the two-level logistic regression model, the chance of occurring DM increases as age of the participants’ increases. It was observed that female participants were more likely to have DM. The occurrence of DM was 62% higher for higher educated participants, 42% higher for the individuals who came from rich family and 63% higher for the individuals having hypertension. The chance of developing diabetes among overweighed people was almost double. However, the individuals engaged in physical work had less chance to have DM. This study calls for greater attention of government and other concerned entities to come up with appropriate policy interventions to lower the risk of DM.

Risk factors associated with wasting among under-5 children residing in urban areas of Bangladesh: a multilevel modelling approach

The main aim of this study was to uncover the risk factors associated with wasting status of under-5 children residing in urban areas of Bangladesh. For analysis purposes, the necessary information was extracted from the Bangladesh Urban Health Survey (BUHS) 2013. The outcome measure was wasting. Chi-square analysis was performed to assess the association between outcome variables and selected factors. Multilevel logistic regression models with a random intercept at each of the individual and regional levels were considered to identify the risk factors of wasting. A total of 10,511 urban children aged 0 to less than 60 months were included in this study. The overall prevalence of wasting was 17.2%. In the bivariate setup, all the selected covariates except child age were found to be significant for wasting status of children (p < 0.05). According to the two-level logistic regression model, the odds of wasting status of children increase with the age of the child and decrease with the increasing level of mother’s education. Compared to children from poor income families, the odds of being wasted were 18% and 47% lower for children coming from middle and rich income families. Among the domains, the odds of having wasted children was higher in the city-corporation slum compared to the city-corporation non-slum. Mothers receiving ANC services had lower odds of having a wasted child. Moreover, a mother who regularly breastfed her baby had 57% lower odds of having a wasted child, compared to a mother who never breastfed her baby. The prevalence of wasting among under-5 children in Bangladesh is still high, and the risk was examined at various multilevel factors. Therefore, top priority should be given to reducing the rate of wasting as a major public health intervention.

Bivariate Dynamic Weighted Survival Entropy of Order 𝛼

Abstract Recently, G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini [G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini, On dynamic weighted survival entropy of order α, Comm. Statist. Theory Methods 46 2017, 5, 2139–2150] proposed a measure of uncertainty based on the survival function called weighted survival entropy of order α. They have also introduced the dynamic form of a measure called dynamic weighted survival entropy of order α and studied various properties in the context of reliability modeling. In this paper, we extend these measures into the bivariate setup and study its properties. We also look into the problem of extending the same measure for conditionally specified models. Empirical and non-parametric estimators are suggested for the proposed measure using the conditionally specified model, and the effect of the proposed estimators is illustrated using simulated and real data sets.

Bivariate Dynamic Weighted Failure Entropy of Order α

SYNOPTIC ABSTRACTRecently, Rohini et al. (2017) proposed a measure of uncertainty based on the distribution function called weighted failure entropy of order α. In this article, we extend the definition of weighted failure entropy of order α to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending weighted failure entropy of order α for conditionally specified models. Several properties are obtained for conditional distributions. Along with some characterization results, it is shown that the proposed measure uniquely determines the distribution function. Moreover, we also proposed an empirical estimator for the new measure.

English

The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.

Factors Associated with Malnutrition among Under-Five Children: Illustration using Bangladesh Demographic and Health Survey, 2014 Data

Child malnutrition remains one of the major public health problems in many parts of the world, especially in a developing country like Bangladesh. Several socioeconomic and demographic factors are responsible for this condition. The present study was conducted to uncover the risk factors associated with malnutrition among under-five children in Bangladesh by analyzing the data from a nationally representative Bangladesh Demographic and Health Survey (BDHS) in 2014. The ordinal dependent variable—child nutrition status (severely malnourished, moderately malnourished, and nourished)—was developed by calculating weight-for-age Z score (WAZ). Bivariate analysis was conducted by performing gamma measure and chi-square test of independence to explore the association between child nutrition status and selected independent variables. To know the adjusted effects of covariates, a popular ordinal model—namely, the proportional odds (PO) model—was considered. All the selected covariates were found highly significant (p < 0.01) in the bivariate setup. However, in the multivariate setup, father’s and mother’s education, wealth index, mother’s body mass index (BMI), and antenatal care service during pregnancy were found highly significant (p < 0.01) factors for child malnutrition. Among the divisions, only Dhaka had more control on child malnutrition, compared to the Sylhet division. Birth interval of children was also reported as a significant factor at a 5% level of significance. Finally, the results of this paper strongly highlighted the necessity of increasing parent’s education level, improving the mother’s nutritional status, and increasing facilities providing antenatal care service in order to achieve better nutrition status among under-five children in Bangladesh.

Bivariate extension of generalized cumulative past entropy

ABSTRACTThe cumulative past entropy (CPE) of order α, a dual measure of cumulative residual entropy (CRE) of order α, has recently been proposed as a suitable extension of CPE. In this article, we extend the definition of (dynamic) CPE of order α (DCPE(α)) to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE(α) for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE(α) are obtained for conditional distributions. Along with some characterization results it is shown that the proposed generalized measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure and prove interrelation with some existing stochastic orders.

International stock market comovement in time and scale outlined with a thick pen

Abstract We quantify time-varying, bivariate and multivariate comovement between international stock market returns, across various time scales, based on a novel approach of Fryzlewicz and Oh (2011) called thick pen transform. With help of this nonparametric and simple tool, we study 11 countries and examine their comovement with respect to (non-dyadic) time scales/frequencies, development and region. We also consider all possible 2036 different combinations of two or more of these countries. In the two-country case, we make comparisons with cross-correlations, either rolling-window or based on the multi-period returns. We find that in the bivariate set-up with the USA, the BRIC countries, except for Brazil (especially over small time scales), offer diversification benefits, while in the multivariate one, clustering with respect to America or Europe (but not Asia) leads to homogeneous groups. Hence development and region cannot always be considered as ultimate clustering factors. Leave-one-out cross-validation shows a nuanced interplay of time scales, development and region as grouping factors for Brazil, Japan, Hong Kong and Russia. Additionally, we provide an example of a time-scale-dependent portfolio strategy.

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

In a recent paper, Kundu et al. (Metrika 79:335–356, 2016) study the notion of cumulative residual inaccuracy (CRI) and cumulative past inaccuracy (CPI) measures in univariate setup as a generalization of cumulative residual entropy and cumulative past entropy, respectively. Here we address the question of extending the definition of CRI (CPI) to bivariate setup and study their properties. We also prolong these measures to conditionally specified models of two components having possibly different ages or failed at different time instants called conditional CRI (CCRI) and conditional CPI (CCPI), respectively. We provide some bounds on using usual stochastic order and investigate several properties of CCRI (CCPI) including the effect of linear transformation. Moreover, we characterize some bivariate distributions.

BIVARIATE DYNAMIC CUMULATIVE RESIDUAL TSALLIS ENTROPY

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

Determination of Influencing Factors for Integrated Pest Management Adoption: A Logistic Regression Analysis

Adoption of an environment friendly agricultural technique, namely Integrated Pest Management (IPM) depends on various socio-economic and demographic factors. This study attempts to determine the factors that influence farmers’ decision to receive IPM. For analysis purpose several socio-economic and demographic information were collect from 617 farmers of five division (Dhaka, Chittagong, Rangpur, Khulna, Barisal), Bangladesh by prepared a structured query. To ensure randomness, simple random sampling technique was used for data collection. Farmers’ ten background characteristics were analyzed in both bivariate and multivariate setup. In bivariate setup, association between selected factors and adoption status of IPM were investigated by performing a chi-square test. To get the adjusted effect, a binary logistic regression model was estimated in multivariate setup. The results of the model provide evidence that farmers’ age, education level, farming experience, training on IPM and membership status of IPM club are the highly significant (P<0.05) factors for IPM adoption. Farm ownership status and Barisal division also found significant (P<0.10) factors for IPM adoption in Bangladesh.

When Can Trend-Cycle Decompositions Be Trusted?

In this paper, we examine the results of GDP trend-cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the best variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend-cycle correlation coefficient and the cycle. We show that the key feature of unemployment that allows for precise estimates of the cycle of GDP is that its nonstationary component is "small" relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2015:Q4, we obtain the trend-cycle decomposition of GDP and find evidence of correlated trend and cycle components and an estimated cycle that is about 2 percent below its trend at the end of the sample.

Chernoff distance for conditionally specified models

Recently, Nair et al. (Stat Pap 52:893–909, 2011) studied Chernoff distance for truncated distributions in univariate setup. The present paper addresses the question of extending the concept of Chernoff distance to bivariate setup with focus on residual as well as past lifetimes. This measure is extended to conditionally specified models of two components having possibly different ages or failed at different time instants. We provide some bounds using likelihood ratio order and investigate several properties of conditional Chernoff distance. The effect of monotone transformation on this conditional measure has also been examined. Moreover, we study conditional Chernoff distance in context of weighted model.

Bivariate extension of (dynamic) cumulative past entropy

ABSTRACTRecently, the concept of cumulative residual entropy (CRE) has been studied by many researchers in higher dimensions. In this article, we extend the definition of (dynamic) cumulative past entropy (DCPE), a dual measure of (dynamic) CRE, to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure.

Simplicial bivariate tests for randomness

This paper introduces a simplex-based extension of the concept of runs to the bivariate setup which allows to test for randomness under the null hypothesis of angularly symmetric distributions. The statistic’s null limiting distribution is derived and Monte Carlo studies evaluate the test performances.

Characterizations of a family of bivariate Pareto distributions

In the present paper, we study properties of a family of bivariate Pareto distributions. The well known dullness property of the univariate Pareto model is extended to the bivariate setup. Two measures of income inequality viz. income gap ratio and mean left proportional residual income are defined in the bivariate case. We also introduce bivariate generalized failure rate useful in reliability analysis. Characterizations, using the above concepts, for various members of the family of bivariate Pareto distributions are derived.