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Shrinkage estimation in the gamma density using prior information is valuable in various fields, including finance, healthcare, and environmental science, where accurate parameter estimation is essential for decision-making and modeling. This manuscript considers the problem of estimation of θ α in Gamma density G(1/θ, p) when the prior estimate or guessed value of the parameter θ α is available in the form of point estimate θ 0 α . Some families of estimators of θ α are defined with its properties. Estimators developed by other authors are identified as particular members of the suggested families of shrinkage estimators. In particular, we have discussed the properties of the suggested families of estimators in an exponential distribution with known coefficient of variation. Numerical illustrations are also given in order to judge the merits of the proposed families of estimators over others. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population mean Y... of the study variable Y using information on population parameters associated with the auxiliary attribute Φ. We have suggested a class of estimators of population Y... mean using auxiliary attribute. Expressions of bias and mean squared error of the suggested class of estimators have been derived up to first order of approximation. Optimum condition is obtained at which the proposed class of estimators has minimum mean squared error. Theoretical findings are also supported through the aid of a numerical illustration. [ABSTRACT FROM AUTHOR]

This article proposes two – stage stratified partial randomized response models based on Tracy and Osahan (1995) model and have large gain in precision. It is also shown that the proposed models are more efficient than Kim and Warde (2004) and Kim and Elam (2005) stratified randomized response models under the conditions presented in the case of completely truthful reporting and less than completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study. [ABSTRACT FROM AUTHOR]

In this paper we have suggested a class of estimators of population mean of sensitive variable under optional randomized response technique as reported in Gupta et al (2014). We have obtained the mean squared error (MSE) of the suggested class of estimators up to the first order of approximation. The optimum conditions are obtained at which the (MSE) of the proposed class of estimators is minimum. An empirical study is carried out to show the performance of the suggested class of estimators over existing estimators .It is found that the performance of proposed class of estimators is better than the existing estimators including Grover and Kaur (2019) [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop more effective methods for estimating population means in sample surveys using auxiliary attributes. To achieve this goal, we introduce a modified version of the estimators proposed by Koyuncu (2013b) and Shahzad et al. (2019), as well as a new class of estimators. We derive expressions for the bias and mean squared error of these new estimators up to the first degree of approximation. Our results show that the suggested classes of estimators perform better than other existing methods, with the lowest mean squared error under optimal conditions. We also conduct an empirical investigation to support our findings. [ABSTRACT FROM AUTHOR]

This manuscript considers the problem of estimating the population mean of the study variable y using information on two auxiliary attributes under simple random sampling without replacement (SRSWOR) scheme. We have defined a class of estimators for population mean based on two auxiliary attributes. We have studied the properties the suggested class of estimators up to first order of approximation. The regions of preferences are obtained under which the proposed class of estimators is more than some existing estimators including Haq and Shabir (2014) estimator. The optimum conditions are obtained at which the proposed class of estimators has the minimum mean squared error. This study is well supported through two numerical data sets. [ABSTRACT FROM AUTHOR]

It is well accepted that suitable additional information improves the efficiency of an estimator but at the same time, it faced the situation of nonresponse. The two-occasion successive sampling is useful to handle the absence of a full response from respondents. In this present study, we have developed exponential estimators for population mean using a subsampling nonrespondent procedure. To show the efficacy of the recommended estimators, several properties are derived, and respective optimum replacement strategies are inferred. To evaluate the performance of the recommended estimators empirically, a computational study is carried out as well. It was found that the recommended estimators outperform the existing ones under the nonresponse in successive sampling. [ABSTRACT FROM AUTHOR]

In this paper we have suggested an exponential estimator of ratio cum product-type for finite population mean in double sampling for stratification. The proposed estimator's bias and mean squared error were obtained up to the first order of approximation. Comparisons have been made theoretically and numerically both with unbiased estimator, ratio and product-type estimator, ratio and product-type exponential estimators. In support of the work, an empirical study is also performed. [ABSTRACT FROM AUTHOR]

This paper suggests a general class of estimators for unknown general population parameter of the study variable using auxiliary information in sample surveys. A large number of estimators of different parameters of the study variable based on auxiliary information can be viewed as a member of the suggested class of estimators. We have derived the bias and mean squared error of the suggested class of estimators under large sample approximation. Optimum conditions are obtained for which the proposed class of estimator has the minimum mean squared error. In particular, a class of estimators for the population mean of the study variable based on the coefficient variation of the auxiliary variable has been derived. The bias and mean squared error of the proposed class of estimators are obtained under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator y ¯ and Das and Tripathi’s (Sankhya C 42(1–2):76–86, 1980) estimator in the context of bivariate normal and bivariate non-normal populations. In support of the present study, an empirical is given. [ABSTRACT FROM AUTHOR]

In this paper we consider a two parameter ratio-product-ratio estimator for estimating population mean in case of post stratification following the estimator due to Chami et al (2012). The bias and mean squared error of proposed estimator are obtained to the first degree of approximation. We derive conditions under which the proposed estimator has smaller mean squared error than the sample mean psy, ratio estimator) (ps R y and product estimators P(ps) y. Empirical studies gives insight on the magnitude of the efficiency of the estimator developed. [ABSTRACT FROM AUTHOR]

In many human surveys, information is in most cases not obtained from all the units in the survey even after some call backs. To cope with this problem, survey statisticians usually consider and adopt the non-respondents sub sampling schemes introduced by Hansen and Hurwitz (1946, Jour. Amer. Statist. Assoc., 41, 517–529). The topic which is of practical importance is the estimation of population mean at the current occasion in two- occasion successive sampling in presence of non-response. In this paper, an alternative to Satici and Kadilar (2011, Hacettepe Jour. Math. Statist. 40(1), 115–124) estimator for the population mean at the current occasion in successive sampling having two occasions is suggested under the missing data case. The minimum mean squared error and optimum fraction of a fresh sample of suggested estimator are obtained. The suggested estimator is compared with the estimator due to Singh and Priyanka (2007, Statistics in Transition. 8(2), 273–292) and Satici and Kadilar (2011, Hacettepe Jour. Math. Statist. 40(1), 115–124) and the efficient conditions for the suggested estimator are obtained. It has been shown theoretically that the proposed class of estimators is more efficient than the Singh and Priyanka (2007) and Satici and Kadilar (2011) estimators. The performance of the suggested class of estimators is examined over Singh and Priyanka (2007) and Satici and Kadilar (2011) estimators with the aid of an empirical study. [ABSTRACT FROM AUTHOR]

This paper aims to discuss the problem of estimating the population mean Y ¯ of the study variable y using information on an auxiliary variable x in circular systematic sampling (CSS) scheme along with the non-response problem. We have suggested a generalized family of estimators for population mean Y ¯ of y based on auxiliary variable x. We have derived the expressions for bias and mean squared error of the proposed family of estimators upto first order of approximation. Optimum conditions are obtained in which the suggested family of estimators has the least mean squared error. It has been shown that the proposed family of estimators is better than usual unbiased estimator, ratio estimator and the regression estimator. An empirical study is provided to show that the suggested family of estimators is better than the ratio and regression estimators. [ABSTRACT FROM AUTHOR]

In this paper we have considered the problem of estimating the population mean using auxiliary information in sample surveys. A class of dual to ratio estimators has been defined. Exact expressions for bias and mean squared error of the suggested class of dual to ratio estimators have been obtained. In particular, properties of some members of the proposed class of dual to ratio estimators have been discussed. It has been shown that the proposed class of estimators is more efficient than the sample mean, ratio estimator, dual to ratio estimator and some members of the suggested class of estimators in some realistic conditions. Some numerical illustrations are given in support of the present study. [ABSTRACT FROM AUTHOR]

In this paper we have considered the problem of estimating the population mean of the sensitive variable using auxiliary information in sample surveys. We have suggested a class of ratio-cum-ratio-type exponential estimator for the population mean of the sensitive variable based on auxiliary variable. We have derived the bias and mean squared error of the proposed class of estimators up to first and second order of approximation. Conditions are obtained in which the suggested class of estimators is more efficient than the usual unbiased estimators, ratio estimator due to Sousa et al. (2010) and ratio-type-exponential estimator. Optimum estimator in the proposed class of estimators is also obtained. Numerical study is carried out in the support of the present study. [ABSTRACT FROM AUTHOR]

In this paper, we have suggested a ratio-ratio-type exponential estimator for finite population mean in double sampling for stratification (DSS). To the first order of approximation the bias and mean squared error of the suggested estimator are obtained and compared theoretically and numerically both with unbiased estimator, ratio and product-type estimator and ratio and product-type exponential estimators. An empirical analysis is also being performed in support of the study. [ABSTRACT FROM AUTHOR]

The crux of the paper is to develop a very general class of estimators for population mean Y ¯ of the study variable y using information on auxiliary variable x in simple random sampling. It has been shown that a large number of known and unknown estimators are members of the suggested class of estimators. Expressions of bias and mean squared errors of the proposed class of estimators have been obtained under large sample approximation. Asymptotic optimum estimator (AOE) in the proposed class of estimators has been obtained with its mean squared error formula. An empirical study is carried out to demonstrate the superiority of the members of the proposed class of estimators over existing estimators. [ABSTRACT FROM AUTHOR]

In this paper, we have suggested a chain ratio-type and a chain ratio-ratio type exponential estimator for estimating the population mean Y of the study variable y in systematic sampling. The properties of the suggested estimators are studied under large sample approximation. Conditions are obtained in which the suggested estimators are better than the systematic sample mean, Yst, ratio estimator Y Rsy in systematic sampling and ratio-type exponential estimator Y Re sy in systematic sampling. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient stratified randomized response model based on Chang et al.'s (2004) model. We have obtained the variance of the proposed estimator of πs, the proportion of the respondents in the population belonging to a sensitive group, under proportional and Neyman allocations. It is shown that the estimator based on the proposed model is more efficient than the Chang et al.'s (2004) estimator under both proportional as well as Neyman allocations, Hong et al.'s (1994) estimator and Kim and Warde's (2004) estimator. Numerical illustration and pictorial representation are given in support of the present study. [ABSTRACT FROM AUTHOR]

For estimating the mean of finite population using information on an auxiliary variable we define the classes of estimators under adoptive cluster sampling in this paper. Expressions for their biases and mean squared errors are obtained under large sample approximation. The minimum mean squared errors of each class of estimators are also given. A similar class of estimators is defined for the variance of the estimator of the mean. A condition is obtained under which the proposed class of estimators of the variance of the estimator is minimum. [ABSTRACT FROM AUTHOR]

In this paper we suggest a ratio type exponential estimator, a chain ratio-type estimator, a chain ratio-type exponential estimator and a chain ratio-ratio-type exponential estimator in cluster sampling. Further we consider a generalized class of chain ratio-ratio-type exponential estimator. The properties of the suggested class of estimators are studied under large sample approximation. Conditions are obtained under which these estimators are more efficient than the usual unbiased estimators. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population mean Y¯ of the study variable y using information on transformed auxiliary variables. In addition to many, Yasmeen et al(2015) estimator shown to be the members of the suggested classes of estimators. We have derived the bias and mean squared error (MSE) of the suggested classes of estimators to the first degree of approximation. We have obtained the optimum conditions for which the suggested classes of estimators have minimum mean squared errors. It has been shown that the proposed classes of estimators are more efficient than the estimators recently envisaged by Yasmeen et al (2015)and other existing estimators. [ABSTRACT FROM AUTHOR]

This paper advocates the problem of estimating the population mean Ȳ of the study variable y using information on two auxiliary variables (x, z). We have suggested a class of estimators for population mean Ȳ of the study variable y based on the knowledge of the population means (X, Z ) of auxiliary variables (x, z), respectively. The bias and mean squared error of the proposed class estimators are obtained under large sample approximation. We have obtained the optimum conditions at which the suggested class of estimators is more efficient than the usual unbiased estimator y , st ratio and product estimators and the one recently proposed by Tailor et al. (2012). An empirical study is carried out in the favour of present study. [ABSTRACT FROM AUTHOR]

This paper suggests a two-parameter ratio-product-ratio type exponential estimator for a finite population mean in simple random sampling without replacement (SRSWOR) following the methodology in the studies of Singh and Espejo (2003) and Chami et al (2012). The bias and mean squared error of the suggested estimator are obtained to the first degree of approximation. The conditions are obtained in which suggested estimator is more efficient than the sample mean, classical ratio and product estimators, ratio-type and product type exponential estimators. An empirical study is given in support of the present study. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the population varianceS2yof the study variableyusing the auxiliary information in sample surveys. We have suggested the (i) chain ratio-type estimator (on the lines of Kadilar and Cingi (2003)), (ii) chain ratio-ratio-type exponential estimator and their generalized version [on the lines of Singh and Pal (2015)] and studied their properties under large sample approximation. Conditions are obtained under which the proposed estimators are more efficient than usual unbiased estimators2yand Isaki (1893) ratio estimator. Improved version of the suggested class of estimators is also given along with its properties. An empirical study is carried out in support of the present study. [ABSTRACT FROM PUBLISHER]

In this paper an estimator of the finite population mean using auxiliary information in sample surveys has been proposed. The bias and mean squared error are obtained under large sample approximation. It has been shown that the proposed estimator performs better than some recently published estimators. [ABSTRACT FROM AUTHOR]

In this paper, we have considered an estimation of the population totalYof the study variabley, making use of information on an auxiliary variablex. A class of estimators for the population totalYusing transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usualPPSestimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the finite population mean Y of the study variable using information on two auxiliary variables (x, z) . A family of ratio-cum-product estimators for population mean Y has been suggested. It has been shown that the usual unbiased estimator y , ratio estimator, product estimator, dual to ratio estimator and dual to product estimator due to Srivenkatramana (1980) and Bandyopadhyaya (1980), Singh et al's (2005, 2011) estimator, Tailor et aTs (2012) estimator, Vishwakarma et al's (2014) estimator and Vishwakarma and Kumar (2015) estimator are members of the suggested family of estimators. In addition to these estimators, various unknown estimators are shown to be the member of the suggested family of estimators. The bias and mean squared error of the proposed family are obtained under large sample approximation. Efficiency comparisons are made to demonstrate the performance of the suggested family over other existing estimators. An empirical study is carried out in support of the present study. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating the finite population meanof the study variableyusing information on an auxiliary variablexin presence of non-response. We have suggested two-parameter ratio-product-ratio estimator in two different situations and their properties are studied under large sample approximation. We have presented comparisons of the proposed two-parameter ratio-product-ratio estimator with usual unbiased estimatorand ratio estimators (tR1,tR2). An empirical study is carried out in support of the present study. [ABSTRACT FROM AUTHOR]

The present paper suggests an interesting and useful ramification of the unrelated randomized response model due to Pal and Singh (2012) [A new unrelated question randomized response model.Statistics46 (1), 99–109] that can be used for any sampling scheme. We have shown theoretically and numerically that the proposed model is more efficient than Pal and Singh (2012) model. [ABSTRACT FROM PUBLISHER]

This paper considers a generalized ratio-cum-product estimator of population mean in systematic sampling using auxiliary information in sample surveys. A large number of estimators of different parameters of the study variables based on auxiliary information can be viewed as a member of suggested class of estimators. The bias and mean squared error of the proposed class of estimator have been obtained under large sample Approximation. Optimum conditions are obtained for which the proposed class of estimators has minimum mean squared error. It has been proved theoretically that the suggested class of estimators at its optimum condition is more different than the regression estimator in systematic sampling. An empirical study is carried out in support of the present study. [ABSTRACT FROM AUTHOR]

In this paper, we have 89 suggested an improved randomized response (RR) model for estimating π, the proportion of respondents in the population belonging to the sensitive group. We have studied the properties of the RR model. The proposed model is found to be more efficient than the RR model studied by Gjestvang and Singh (2006). Numerical illustration is given in support of the present study. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population proportion π of a sensitive group. We have suggested a randomized response (RR) model that is more efficient than the one envisaged by Gjestvang and Singh ([2006), A new randomized response model, Journal of Royal Statistcal Socity, B, (3), 523–530]. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population mean of a sensitive variable in presence of scrambled response. We have suggested a randomized response model which uses known values of mean and variance of scrambling variable. We have shown that the proposed randomized response model is always better than that of Gjestvang and Singh's (2009) and Singh and Tarray's (2014) randomized response models. A numerical study for efficiency comparison is also presented. [ABSTRACT FROM AUTHOR]

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This article addresses the problem of estimating the proportion πS of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is more efficient than Kim and Warde stratified randomized response model and Mangat model. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population varianceS2yof the study variableyusing auxiliary information in sample surveys. We have suggested a class of estimators of the population varianceS2yof the study variableywhen the population varianceS2xof the auxiliary variablexis known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration. [ABSTRACT FROM AUTHOR]

In the present article, we have proposed some classes of estimators based on transformed auxiliary variable. The biases and mean squared errors (MSEs) of the proposed estimators have been obtained. The proposed estimators have been compared with simple mean estimator when there is no matching and the optimum estimator, which is a combination of the means of the matched and unmatched portion of the sample at the second occasion. Optimum replacement policy and the efficiency of the proposed estimators have been discussed. Theoretical results are well supported with an empirical study. [ABSTRACT FROM AUTHOR]

This paper intends to put emphasis on the role of two auxiliary variables on both the occasions to improve the precision of estimates at current (second)occasion in two-occasion successive sampling. There are different situations when (i) the information on the single auxiliary variablez1is readily available on both the occasions and positively correlated with the study variabley, (ii) the information on the single auxiliary variablez2is readily available on both the occasions and negatively correlated with the study variabley, (iii) the information on two auxiliary variables (z1,z2) are available on both the occasions, with one auxiliary variablez1is positively correlated and the other negatively correlated with the study variabley; these have been discussed through proposing three estimators (one in each situation) of the population meanon the current (second) occasion and analyzing their properties. The properties of the proposed estimators have been studied and compared with the sample mean estimator when there is no matching from the previous occasion and traditional successive sampling estimator, which is a linear combination of the means of the matched and unmatched portion of the sample at the current (second) occasion. Optimal replacement policy is discussed. Empirical studies are carried out to show the domination of the recommended estimators. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating a general parameter using information on an auxiliary variableX. We have suggested a class of exponential-type ratio estimators for the parameter and its properties are studied. It is identified that the estimators due to Upadhyaya et al. [Journal of Statistical Theory and Practice (2011), 5(2), 285–302] and Yadav and Kadilar [Revista Columbiana de Estadistica, (2013), 36(1), 145–152] are members of the proposed estimator. We have also shown that the suggested estimator is more efficient than the estimators of Upadhyaya et al. (2011) and Yadav and Kadilar (2013). Numerical illustration is provided in support of the present study. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the population total of the sensitive variable under a unified approach. Odumade and Singh (2008) have suggested a forced quantitative randomized response model and then suggested an unbiased estimator of the population total Y of the sensitive variable y. It is observed that the optimum estimator of the population total Y due to Odumade and Singh (2008) depends on the unknown population parameter under investigation which lacks the practical utility. To overcome this drawback Odumade and Singh (2008) suggested another unbiased estimator of the population total of the sensitive variable based on two independent samples which causes the increase in the cost. Keeping this in view we define an alternative randomized response procedure and hence the estimator of the population total of the sensitive variable based on one sample only which is free from such limitation and more efficient than the Odumade and Singh (2008) estimator. The relative efficiency of the proposed estimator with respect to Bar-Lev et al. (2004) and Odumade and Singh (2008) estimators are examined through numerical illustration. [ABSTRACT FROM AUTHOR]

This paper suggests a new stratified randomized response model based on Kuk's [Biometrika (1990), 77, 2, pp.436–438] model that has Neyman allocation and considerable gain in precision. It has been identified that the stratified randomized response models due to Kim and Warde (2004), Kim and Elam's (2005), and Kim and Elam's (2007) are members of the proposed model. It is shown that the proposed model is more efficient than Kuk's (1990) model both theoretically and empirically. The results of this paper are also extended in the situation when trials are repeated. [ABSTRACT FROM AUTHOR]

Taking clue from the pioneer work of Singh and Sedory (2013), we have suggested a new stratified randomized response (RR) model. The properties of the suggested stratified RR model have been studied under proportional and “Neyman” allocations. The study has been also carried out in the presence of crude prior estimates. Numerical illustrations are also given in support of the present study. [ABSTRACT FROM AUTHOR]

The crux of this article is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1991) randomization device by utilizing the Poisson distribution in simple random sampling and stratified sampling. Properties of the proposed randomized response (RR) model have been studied along with recommendations. It is also shown that the proposed model is more efficient than that of Land et al. (2011) in simple random sampling and that of Lee et al. (2013) in stratified random sampling when the proportion of persons possessing a rare unrelated attribute is known. Numerical illustrations are also given in support of the present study. [ABSTRACT FROM AUTHOR]

This article suggests the class of estimators of population mean of study variable using various parameters related to an auxiliary variable with its properties in simple random sampling. It has been identified that the some existing estimator/classes of estimators are members of suggested class. It has been found theoretically as well as empirically that the suggested class is better than the existing methods. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating the population mean on the current (second) occasion using multi-auxiliary information in successive sampling over two occasions. A general class of estimators is proposed for estimating population mean on the current occasion and expressions for bias and mean square error for these estimators are obtained up to first degree of approximation. The minimum variance bound estimator in the proposed class is discussed. Many popular estimators have been shown to belong to this class. Optimum replacement policy is also discussed. Finally, the superiority of the proposed class of estimators over multivariate version of chain type ratio estimator envisaged by Singh (2005) is established empirically. [ABSTRACT FROM AUTHOR]

This paper aimed at providing an efficient new unbiased estimator for estimating the proportion of a potentially sensitive attribute in survey sampling. The suggested randomization device makes use of the means, variances of scrambling variables, and the two scalars lie between “zero” and “one.” Thus, the same amount of information has been used at the estimation stage. The variance formula of the suggested estimator has been obtained. We have compared the proposed unbiased estimator with that of Kuk (1990) and Franklin (1989), and Singh and Chen (2009) estimators. Relevant conditions are obtained in which the proposed estimator is more efficient than Kuk (1990) and Franklin (1989) and Singh and Chen (2009) estimators. The optimum estimator (OE) in the proposed class of estimators has been identified which finally depends on moments ratios of the scrambling variables. The variance of the optimum estimator has been obtained and compared with that of the Kuk (1990) and Franklin (1989) estimator and Singh and Chen (2009) estimator. It is interesting to mention that the “optimum estimator” of the class of estimators due to Singh and Chen (2009) depends on the parameter π under investigation which limits the use of Singh and Chen (2009) OE in practice while the proposed OE in this paper is free from such a constraint. The proposed OE depends only on the moments ratios of scrambling variables. This is an advantage over the Singh and Chen (2009) estimator. Numerical illustrations are given in the support of the present study when the scrambling variables follow normal distribution. Theoretical and empirical results are very sound and quite illuminating in the favor of the present study. [ABSTRACT FROM PUBLISHER]