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Purpose: The Indian pharmaceutical industry currently faces multiple challenges, including rising costs and slowing export growth, which in turn have limited its ability to expand presence in global canvas. Given the nature of sectoral dynamics, a pharmaceutical firm must undertake huge investments in R&D to introduce product innovation, in turn enhancing market share and sustaining profit streams. The development of novel medicines, confirmed by the granting of patent rights, provides a pharma company edge over its competitors. In addition, presence of innovator firms within the industry invigorates the sectoral value chain and raises efficiency. Hence, it is important to analyze whether granting patent rights enhances the exports of pharmaceutical products in the Indian context. Design/methodology/approach: The current study explored this question using a simultaneous-equation framework. Specifically, the authors use the methods developed by Davidson and MacKinnon (1993) and Greene (2003) to obtain heteroscedasticity-consistent estimates. The time-series properties of the data were further probed, and robust estimates were used to test the theory. Methods developed by Baltagi (1981) have been used further to refine the authors' estimations. Findings: After controlling for relevant variables, it is observed that granting of patents caused a significantly positive impact on pharmaceutical exports. Furthermore, the change in the patent administration regime had a significant impact on patent fillings, which further impacted their exportability. Compared to patents granted patents filed had a higher impact on pharmaceutical exports. Originality/value: This study attempts to apply the framework developed by Goldstein and Khan (1978) with necessary modifications to suit the context of a developing country. The application of the 3SLS method to estimate the export supply equation for pharmaceutical products is a novel approach to the research question in general and to the Indian context in particular. System autocorrelation and heteroscedasticity tests were performed to refine the results further. [ABSTRACT FROM AUTHOR]

In the literature, estimation of weighted extropy is infrequently considered. In this paper, some non-parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators is demonstrated using real data sets. [ABSTRACT FROM AUTHOR]

The stop-loss moments have generally been used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies, the investigator cannot record the sampling units with equal probability, and in such a scenario, the selected sample units appear with unequal probability, in other words with different weights, which leads to a biased or weighted sampling. In the present study, we examine the usefulness of stop-loss moments in biased sampling. The application of the weighted stop-loss moments in analyzing biased data has been investigated and compared using different empirical estimators through simulated and real data sets. [ABSTRACT FROM AUTHOR]

In the literature, estimation of weighted extropy is infrequently considered. In this paper, some non-parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators is demonstrated using real data sets.

This paper deals with finite nonzero‐sum Markov games under a discounted optimality criterion and infinite horizon. The state process evolves according to a stochastic difference equation and depends on players' actions as well as a random disturbance whose distribution is unknown to the players. The actions, the states, and the values of the disturbance are observed by the players, then they use the empirical distribution of the disturbances to estimate the true distribution and make choices based on the available information. In this context, we propose an almost surely convergent procedure—possibly after passing to a subsequence—to approximate Nash equilibria of the Markov game with the true distribution of the random disturbance. [ABSTRACT FROM AUTHOR]

Background & Aims: Bioelectrical impedance analysis (BIA) for body composition estimation is increasingly used in clinical and field settings to guide nutrition and training programs. Due to variations among BIA devices and the proprietary prediction equations used, studies have recommended the use of raw measures of resistance (R) and reactance (X c ) within population-specific equations to predict body composition., Objective: We compared raw measures from three BIA devices to assess inter-device variation and the impact of differences on body composition estimations., Methods: Raw R, X c , impedance (Z) parameters were measured on a calibrated phantom and athletes using tetrapolar supine (BIA SUP4 ), octapolar supine (BIA SUP8 ), and octapolar standing (BIA STA8 ) devices. Measures of R and Xc were compared across devices and graphed using BIA vector analysis (BIVA) and raw parameters were entered into recommended athlete-specific equations for predicting fat-free mass (FFM) and appendicular lean soft tissue (ALST). Whole-body FFM and regional ALST were compared across devices and to a criterion five-compartment (5C) model and dual energy X-ray absorptiometry for ALST., Results: Data from 73 (23.2 ± 4.8 y) athletes were included in the analyses. Technical differences were observed between Z (range 12.2-50.1Ω) measures on the calibrated phantom. Differences in whole-body impedance were apparent due to posture (technological) and electrode placement (biological) factors. This resulted in raw measures for all three devices showing greater dehydration on BIVA compared to published norms for athletes using a separate BIA device. Compared to the 5C FFM, significant differences (p < 0.05) were observed on all three equations for BIA SUP8 and BIA STA8 , with constant error (CE) from -2.7 to -4.6 kg; no difference was observed for BIA SUP4 or when device-specific algorithms were used. Published equations resulted in differences as large as 8.8 kg FFM among BIA devices. For ALST, even after a correction in the error of the published empirical equation, all three devices showed significant (p < 0.01) CE from -1.6 to -2.9 kg., Conclusions: Raw bioimpedance measurements differ among devices due to technical, technological, and biological factors, limiting interchangeability of data across BIA systems. Professionals should be aware of these factors when purchasing systems, comparing data to published reference ranges, or when applying published empirical body composition prediction equations., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: John Shepherd reports financial support was provided by Hologic Inc. Steven Heymsfield reports a relationship with Tanita Corporation that includes: board membership. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Published by Elsevier Ltd.)

The work deals with a class of discrete‐time zero‐sum Markov games under a discounted optimality criterion with random state‐action‐dependent discount factors of the form α˜(xn,an,bn,ξn+1), where xn,an,bn, and ξn+1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. The one‐stage payoff is assumed to be possibly unbounded. In addition, the process {ξn} is formed by observable, independent, and identically distributed random variables with common distribution θ, which is unknown to players. By using the empirical distribution to estimate θ, we introduce a procedure to approximate the value V∗ of the game; such a procedure yields construction schemes of stationary optimal strategies and asymptotically optimal Markov strategies. [ABSTRACT FROM AUTHOR]

There exists a rich empirical literature on the presence of intra-industry trade (IIT), i.e., simultaneous exports and imports within the same product groups and its determinants, both in the context of developed and developing countries. With deepening of Global Value Chains (GVCs) and International Production Networks (IPNs) across the globe, a rise in IIT has generally been noticed and India is no exception to this trend. The current paper analyses India's IIT in select sectors and decomposes the same in Vertical IIT (VIIT) and Horizontal IIT (HIIT) categories in terms of product quality, using trade data at the HS 6-digit level. It is observed that India's IIT is predominantly vertical in nature. India's VIIT has increased significantly over 2001-18 in select sectors, barring the exception of base-metals and iron-steel segments. The analysis next focuses on the determinants of India's VIIT during 2001-15 in a panel data framework by considering both country-specific and sectorspecific factors. The empirical results reveal that increase in capitalintensity, higher skill-intensity of workforce, multilateral as well as regional trade policy reforms, higher research and development orientation, trade facilitation measures and decline in industrial concentration facilitates India's cross-sector VIIT pattern. The interaction terms in the model indicates that growing sophistication in production may create greater scope for trade in vertically differentiated products. The results have interesting implications for India's recent manufacturing sector policy framework, particularly the 'Make-in-India' initiative. [ABSTRACT FROM AUTHOR]

Abstract Cryptocrystalline flint is an extremely hard siliceous rock that is found in chalk formations. The chalk is frequently a prefered rock type, which in recent decades is often used as a host for underground rock caverns and tunnels in Europe and North America. A reliable estimation of the uniaxial compressive strength (UCS) of the extremely strong flint, with an average UCS of about 600 MPa will provide guidance for a proper engineering design, where flint is encountered, thereby avoiding project progress delay, litigation as well as economic consequences. Conventional UCS measurement using core samples is cumbersome for flint due to the extreme strength and hardness of the rock, for which the core sample preparation process is often extremely difficult. In this study, the UCS prediction models of flints collected from the North-West Europe were developed and the validity of the developed models was investigated. A series of laboratory index tests (comprising the three-point-bending, point load, ultrasonic velocity, density, Shore hardness and Cerchar Abrasivity tests) were perfomed. The index test results were correlated with the UCS values previously determined in the laboratory using both cylindrical and cuboidal specimens to develop the UCS prediction models. Regression analysis of the UCS and the index test results was then performed to evaluate for any potential correlations that can be applied to estimate the UCS of the cryptocrystalline flint. Intensive validity and comparison studies were performed to assess the performance of the proposed UCS prediction models. This study showed that UCS of the tested flint is linearly correlated with its point load strength index, tensile strength and compressional velocity, and is parabolically correlated with its density. The present study also demonstrated that only a couple of the previously developed empirical UCS models for estimating UCS are suitable for flint, which should be used with care. Highlights • An experimental study of the mechanical and mineralogical properties of cryptocrystalline flint. • Assessment and development of UCS prediction models for the extremely strong cryptocrystalline flint. • Validity study of the proposed models, and comparison between measured and estimated UCS. [ABSTRACT FROM AUTHOR]

The replacement I-35W bridge in Minneapolis saw less traffic than the original bridge though it provided substantial travel time saving for many travelers. This observation cannot be explained by the classical route choice assumption that travelers always take the shortest path. Accordingly, a boundedly rational route switching model is proposed assuming that travelers will not switch to the new bridge unless travel time saving goes beyond a threshold or 'indifference band'. Indifference bands are assumed to follow lognormal distribution and are estimated in two specifications: the first one assumes every driver's indifference band is drawn from a population indifference band and the second one assumes that the mean of drivers' indifference bands is a function of their own characteristics. Route choices of 78 subjects from a GPS travel behavior study were analyzed before and after the addition of the new I-35W bridge to estimate parameters. This study provides insights into empirical analysis of bounded rationality and sheds light on indifference band estimation using empirical data. [ABSTRACT FROM AUTHOR]

This work deals with a class of discrete-time zero-sum Markov games whose state process {xt} evolves according to the equation xt+1 = F(xt; at; bt; ξt); where at and bt represent the actions of player 1 and 2, respectively, and fξtg is a sequence of independent and identically distributed random variables with unknown distribution θ. Assuming possibly unbounded payo ff, and using the empirical distribution to estimate θ. we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria. [ABSTRACT FROM AUTHOR]

In the dynamic power management (DPM), it is quite important to switch a high-power consuming state to a low-power consuming one at a suitable timing. This problem has been formulated as Markov decision processes (MDPs) with state-dependent control in the past literature. However, this approach may not be often feasible in many practical situations, because the state-dependent policy requires that all the states on a request arrival process must be observed through an online monitoring. To overcome this problem, we develop a simple time-out policy in the DPM, which can be regarded as the optimal timing to take a GO-SLEEP action during an idle period of the transaction system. We derive the optimal time-out policy minimizing the expected power consumption per unit time in the steady state analytically under the assumption that the request arrival process is given by a Markovian arrival process with an arbitrary number of phases. In numerical experiments with real read/write data for a hard disk unit and CPU utilization data, we estimate the expected power consumption per unit time under two DPM policies, namely, the time-out policy and the MDP-based policy, and quantitatively compare their effectiveness on the power reduction. [ABSTRACT FROM PUBLISHER]

Gupta and Kirmani (2008) showed that theconvex conditional mean function(CCMF) characterizes the distribution function completely. In this paper, we introduce a consistent estimator of CCMF and call itempirical convex conditional mean function(ECCMF). Then we construct a simple consistent test of fit based on the integrated squared difference between ECCMF and CCMF. The theoretical and asymptotic properties of the estimator ECCMF and the proposed test statistic are studied. The performance of the constructed test is investigated under different distributions using simulations. [ABSTRACT FROM PUBLISHER]

In thiswork,we extend some parameters built on a probability distribution introduced before to the casewhere the proximity between real numbers is measured by using a Bregman divergence. This leads to the definition of the Bregman superquantile (thatwe can connect with severalworks in economy, see for example [18] or [9]). Axioms of a coherent measure of risk discussed previously (see [31] or [3]) are studied in the case of Bregman superquantile. Furthermore,we deal with asymptotic properties of aMonte Carlo estimator of the Bregman superquantile. Several numerical tests confirm the theoretical results and an application illustrates the potential interests of the Bregman superquantile.

The vehicle routing problem with stochastic demands and customers (VRPSDC) requires finding the optimal route for a capacitated vehicle that delivers goods to a set of customers, where each customer has a fixed probability of requiring being visited and a stochastic demand. For large instances, the evaluation of the cost function is a primary bottleneck when searching for high quality solutions within a limited computation time. We tackle this issue by using an empirical estimation approach. Moreover, we adopt a recently developed state-of-the-art iterative improvement algorithm for the closely related probabilistic traveling salesman problem. We integrate these two components into several metaheuristics and we show that they outperform substantially the current best algorithm for this problem. [ABSTRACT FROM AUTHOR]

Pore size distribution is an important factor that affects the moisture diffusion and permeability properties of cement-based materials. For cement paste, it is assumed that the mesopores (100 nm-0.01 mm) and macropores (0.01 mm-1 cm) can be neglected compared to the micropores (). Based on the surface energy theory, moisture chemical potential of pore water is introduced to explain the liquid-gas equilibrium in pores with different radius. Using chemical potential as an intermedium, a quantitative relationship between micropore size distribution and water adsorption isotherms can be established. The micropore size distribution can be treated as an explanation of the moisture adsorption behavior, and by using adsorption isotherms, the micropore size distribution can be estimated conveniently. Mortar and concrete can be regarded as a combination of cement paste and aggregates; thus, besides the micropores, the mesopores and macropores are also taken into consideration. Finally, the general empirical estimation equations for pore-size distribution are developed for cement, mortar, and concrete, which can be used for refined modeling and simulating of durability-related issues, such as frost action, water permeability, and drying shrinkage. [ABSTRACT FROM AUTHOR]

The aim of the study is to calculate the price elasticity of demand for several local public transport products of a mid-sized German city (Jena) to estimate the potential subsidy requirements of social tariff concessions. The results of the ten year time series AR-model estimation show an elasticity coefficient of − 0.63 for a single ticket which is slightly higher in absolute terms compared with past studies but can be explained with the geographical structure of the examined city. The price elasticity of social concession-tariffs is significantly higher. This means that the income effect will be outweighed by the effect of lower demand of welfare recipients for (relatively inelastic) intra-city commuting.

How will consumption patterns for popular and "long-tail" products change when consumers move from brick-and-mortar to Internet markets? We address this question using customer-level panel data obtained from a national video rental chain as it was closing many of its local stores. These data allow us to use the closure of a consumer's local video store as an instrument, breaking the inherent endogeneity between channel choice and product choice. Our results suggest that when consumers move from brick-and-mortar to online channels, they are significantly more likely to rent "niche" titles relative to "blockbusters." This suggests that a significant amount of niche product consumption online is due to the direct influence of the channel on consumer behavior, not just due to selection effects from the types of consumers who decide to use the Internet channel or the types of products that consumers decide to purchase online. [ABSTRACT FROM AUTHOR]

Pollution load and contamination levels of phthalate esters (PAEs) in agricultural soils throughout China were studied in this work. The usage amount and residual rates of plastic film were the main factors explaining the variation among regions and leading to higher pollution load and contamination levels in agricultural big provinces. However, higher pollution loads and contamination levels frequently occurred under non-recycling than recycling scenarios during calculation. Extremely high loads (more than 10 kg/ha/year) of PAEs were estimated in five areas including Beijing city, Tibet, Liaoning Province, Jilin Province and Fujian Province and the high contamination levels in agricultural soil were presented in these places with more than 4.0 mg/kg under non-recycling scenarios. The predicted concentrations of PAEs in soils exceed the target value for soils from Netherlands (ΣPAEs = 0.1 mg/kg), indicating very high contamination of most Chinese agricultural soils. Significant differences in estimation results after plastic film utilization suggest that decreasing plastic film residue after application is an effective measure to control PAE pollution in soils. However, the comparison between contamination levels of PAEs estimated by the model and the previous detections of PAEs pollution levels in agricultural soils showed that there were presented wide range of PAE sources indicated to agricultural soils. [ABSTRACT FROM AUTHOR]

In this work we present an extensive simulation study on Mallows distance in the context of Gaussian and non Gaussian VARFIMA processes. Our main goal is to analyze the dependence among the components of VARFIMA processes through the Mallows distance point of view. A possible relationship between the Mallows distance and the fractional differencing parameter d , the type and level of dependence in the innovation process as well as its marginal behavior is investigated. We study the behavior of the Kendall's τ dependence coefficient under the same framework for comparison purposes. For the Mallows distance, we consider an estimator based on the empirical marginal distribution function. Based on our simulation results, we propose both a semiparametric estimator for the fractional differencing parameter and a testing procedure to assess the presence of strong long range dependence in the components of VARFIMA processes of any (finite) dimension. [ABSTRACT FROM AUTHOR]

This study addresses the product investment decision faced by firms in the rent-to-own industry. In this setting, a customer arrives according to a random process and requests one unit of a product to rent (and eventually own should he/she choose to make all the required payments). At the time of request, if the product is available in inventory, the firm enters into a contractual agreement (by accepting the customer's offer) and rents the merchandise. More interesting and the case considered here, if the requested item is not in inventory, the firm must decide whether to purchase the item in order to rent it out or to simply reject the request. The customer's offer specifies the desired maximum contract length and the payment frequency--from which the firm determines the fixed periodic payment charged. The firm makes its investment decision based on the characteristics of the offer as well as those of the product (eg, initial and resale values, useful life and carrying costs) in essence performing a complicated cost benefit analysis. An extension is also considered whereby instead of simply rejecting the request the firm can adjust the required payment amount. Dynamic programming techniques are used to address the problem and to solve for the firm's optimal decision. [ABSTRACT FROM AUTHOR]

In order to study the reliability of the empirical estimation of joint shear strength by the JRC (joint roughness coefficient)-JCS (joint compressive strength) model, natural rock joints of different lithologic characteristics and different sizes were selected as samples, and their shear strengths under dry and saturated conditions were measured by direct shear test and compared to those estimated by the JRC-JCS model. Comparison results show that for natural rock joints with joint surfaces closely matched, the average relative error of joint shear strength between empirical estimation and direct shear test is 9.9%; the reliability of the empirical estimation of joint shear strength by the JRC-JCS model is good under both dry and saturated conditions if the JRC is determined accounting for directional statistical measurements, scale effect and surface smoothing during shearing. However, for natural rock joints with joint surfaces mismatched, the average relative error of joint shear strength between empirical estimation and direct shear test is 39.9%; the reliability of empirical estimation of joint shear strength by the JRC-JCS model is questionable under both dry and saturated conditions. [ABSTRACT FROM AUTHOR]

We present a Jason-2 sea state bias (SSB) model from the first year of GDR products along with updates of Jason-1, TOPEX-A, and TOPEX-B solutions. Our re-evaluation of the Jason-1 SSB focused on data from the new version (C) of the GDR while for TOPEX, the updated solutions benefited from the availability of both a set of new precise orbits that are consistent with Jason-2 and an updated set of state-of-the-art geophysical corrections. Therefore, derived from homogeneous sea surface height (SSH) data to minimize geographically correlated SSH differences between missions, these empirical SSB models contribute to the consistency between Jason-2 and Jason-1 SSH data and between TOPEX and Jason-1 data during their respective tandem phase and thus to the stability of the whole altimetry system over the past 17-year period. [ABSTRACT FROM AUTHOR]

The National Collegiate Athletic Association (NCAA) college football ranking, in which the so-called national champion is determined, has been plagued by controversies the last few years. The difficulty arises because there is a need to make a complete ranking of teams even though each team has a different schedule of games with a different set of opponents. A similar problem arises whenever one wants to establish a ranking of patents or academic journals, etc. This article develops a simple consistent weighted ranking (CWR) scheme in which the importance of (weights on) every success and failure are endogenously determined by the ranking procedure. This consistency requirement does not uniquely determine the ranking, as the ranking also depends on a set of parameters relevant for each problem. For sports rankings, the parameters reflect the importance of winning vs. losing, the strength of schedule, and the relative importance of home vs. away games. Rather than assign exogenous values to these parameters, we estimate them as part of the ranking procedure. The NCAA college football has a special structure that enables the evaluation of each ranking scheme and hence, the estimation of the parameters. Each season is essentially divided into two parts: the regular season and the postseason bowl games. If a ranking scheme is accurate, it should correctly predict a relatively large number of the bowl game outcomes. We use this structure to estimate the four parameters of our ranking function using ''historical'' data from the 1999-2003 seasons. Finally, we use the parameters that were estimated and the outcome of the 2004-2006 regular seasons to rank the teams each year for 2004-2006. We then calculate the number of bowl games whose outcomes were correctly predicted following the 2004-2006 season. None of the six ranking schemes used A by the Bowl Championship Series (BCS) predicted more bowl games correctly over the 2004-2006 period than our CWR scheme. [ABSTRACT FROM AUTHOR]

Joint roughness coefficient ( JRC) is the key parameter for the empirical estimation of joint shear strength by using the JRC- JCS (joint wall compressive strength) model. Because JRC has such characteristics as nonuniformity, anisotropy, and unhomogeneity, directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method. However, the directional statistical measurement of JRC is time-consuming. In order to present an ideal measurement method of JRC, new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC. Operation methods of the profilographs and roughness rulers were also introduced. A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC. [ABSTRACT FROM AUTHOR]

The use of ant colony optimization for solving stochastic optimization problems has received a significant amount of attention in recent years. In this paper, we present a study of enhanced ant colony optimization algorithms for tackling a stochastic optimization problem, the probabilistic traveling salesman problem. In particular, we propose an empirical estimation approach to evaluate the cost of the solutions constructed by the ants. Moreover, we use a recent estimation-based iterative improvement algorithm as a local search. Experimental results on a large number of problem instances show that the proposed ant colony optimization algorithms outperform the current best algorithm tailored to solve the given problem, which also happened to be an ant colony optimization algorithm. As a consequence, we have obtained a new state-of-the-art ant colony optimization algorithm for the probabilistic traveling salesman problem. [ABSTRACT FROM AUTHOR]

We propose a class of power-transformed linear quantile regression models for survival data subject to random censoring. The estimation procedure follows two sequential steps. First, for a given transformation parameter, we can easily obtain the estimates for the regression coefficients by minimizing a well-defined convex objective function. Second, we can estimate the transformation parameter based on a model discrepancy measure by constructing cumulative sum processes. We show that both the regression and transformation parameter estimates are strongly consistent and asymptotically normal. The variance-covariance matrix depends on the unknown density function of the error term, so we estimate the variance by the usual bootstrap approach. We examine the performance of the proposed method for finite sample sizes through simulation studies and illustrate it with a real data example. [ABSTRACT FROM AUTHOR]

We consider here ergodic homogeneous Markov chains with countable state spaces. The entropy rate of the chain is an explicit function of its transition and stationary distributions. We construct estimators for this entropy rate and for the entropy of the stationary distribution of the chain, in the parametric and nonparametric cases. We study estimation from one sample with long length and from many independent samples with given length. In the parametric case, the estimators are deduced by plug-in from the maximum likelihood estimator of the parameter. In the nonparametric case, the estimators are deduced by plug-in from the empirical estimators of the transition and stationary distributions. They are proven to have good asymptotic properties. [ABSTRACT FROM AUTHOR]

Simple yet accurate techniques for estimating system parallel resonant frequencies are presented. The proposed techniques make use of existing power quality data, specifically those of capacitor switching transients, to determine frequency estimates. A detailed representation of the system including the data required to develop device models (transmission lines, transformers, loads, etc.) is not required. The efficacy and pitfalls of the technique was demonstrated using power quality data collected at transmission and distribution systems where resonant frequencies were known so as to identify the best application environment of the technique. Frequency estimation results correspond closely to actual system resonant frequencies. [ABSTRACT FROM PUBLISHER]

The stop-loss moments have generally been used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies, the investigator cannot record the sampling units with equal probability, and in such a scenario, the selected sample units appear with unequal probability, in other words with different weights, which leads to a biased or weighted sampling. In the present study, we examine the usefulness of stop-loss moments in biased sampling. The application of the weighted stop-loss moments in analyzing biased data has been investigated and compared using different empirical estimators through simulated and real data sets., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)