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Variance Estimation Using Median of the Auxiliary Variable
International Journal of Probability and Statistics , 2012, DOI: 10.5923/j.ijps.20120103.02
Abstract: The present paper deals with a modified ratio type variance estimator for estimation of population variance of the study variable, when the population median of the auxiliary variable is known. The bias and the mean squared error of the proposed estimator are obtained and also derived the conditions for which the proposed estimator performs better than the traditional ratio type variance estimator suggested by Isaki[10] and the modified ratio type variance estimators suggested by Kadilar and Cingi[11]. Further we have compared the efficiencies of the proposed estimator with that of traditional ratio type variance estimator and existing modified ratio type variance estimators for certain known populations. From the numerical study it is observed that the proposed estimator performs better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.
Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis
American Journal of Mathematics and Statistics , 2012, DOI: 10.5923/j.ajms.20120204.05
Abstract: The present paper deals with two modified ratio estimators for estimation of population mean of the study variable using the linear combination of the known population values of the Median and the Co-efficient of Kurtosis of the auxiliary variable. The biases and the mean squared errors of the proposed estimators are derived and are compared with that of existing modified ratio estimators for certain natural populations. Further we have also derived the conditions for which the proposed estimators perform better than the existing modified ratio estimators. From the numerical study it is also observed that the proposed modified ratio estimators perform better than the existing modified ratio estimators.
A Class of Modified Ratio Estimators Using Deciles of an Auxiliary Variable
International Journal of Statistics and Applications , 2012, DOI: 10.5923/j.statistics.20120206.02
Abstract: In the past, a number of modified ratio estimators are suggested for estimation of the population mean of the study variable using Co-efficient of Variation, Co-efficient of Kurtosis, Co-efficient of Skewness, Population Correlation Coefficient, Median, Quartile and their linear combinations of the auxiliary variable. However no attempt is made to use the deciles, which are more generalized version of quartiles and Median. Hence an attempt is made in this paper to use the deciles in the modified ratio estimators for estimation of population mean of the study variable when the population deciles of the auxiliary variable are known. The biases and the mean squared errors of the proposed estimators are derived and are compared with that of existing modified ratio estimators for certain known populations. Further we have also derived the conditions for which the proposed estimators perform better than the existing modified ratio estimators. From the numerical study it is observed that the proposed modified ratio estimators perform better than the existing modified ratio estimators.
Variance Estimation Using Quartiles and their Functions of an Auxiliary Variable
International Journal of Statistics and Applications , 2012, DOI: 10.5923/j.statistics.20120205.04
Abstract: In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using Quartiles and their functions of the auxiliary variable are known. The biases and mean squared errors of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of traditional ratio type variance estimator and existing modified ratio type variance estimators for certain known populations. From the numerical study it is observed that the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.
Use of Auxiliary Information in Variance Estimation  [PDF]
Jayant Singh,Viplav K. Singh,Sachin Malik,Rajesh Singh
Statistics , 2013,
Abstract: This paper proposes a class of ratio type estimators of finite population variance, when the population variance of an auxiliary character is known. Asymptotic expression for mean square error (MSE) is derived and compared with the mean square errors of some existing estimators. An empirical study is carried out to illustrate the performance of the constructed estimator over others.
Scaled variance, skewness, and kurtosis near the critical point of nuclear matter  [PDF]
V. Vovchenko,D. V. Anchishkin,M. I. Gorenstein,R. V. Poberezhnyuk
Physics , 2015, DOI: 10.1103/PhysRevC.92.054901
Abstract: The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, the almost zero skewness, and the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point, namely, they both may attain large positive or negative values.
Estimating the mean and variance from the median, range, and the size of a sample
Stela Hozo, Benjamin Djulbegovic, Iztok Hozo
BMC Medical Research Methodology , 2005, DOI: 10.1186/1471-2288-5-13
Abstract: In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data.We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 70), the formula range/6 gives the best estimator for the standard deviation (variance).We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy.Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported.To perform meta-analysis of continuous data, the meta-analysts need the mean value and the variance (or standard deviation) in order to pool data. However, sometimes, the published reports of clinical trials only report the median, range and the size of the trial. In this article we use simple and elementary inequalities in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. In fact, the value of our approximation(s) is in giving a method for estimating the mean
Estimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable
International Journal of Probability and Statistics , 2012, DOI: 10.5923/j.ijps.20120104.04
Abstract: The present paper deals with a class of modified ratio estimators for estimation of population mean of the study variable using the linear combination of the known values of the Co-efficient of Variation and the Median of the auxiliary variable. The biases and the mean squared errors of the proposed estimators are derived and are compared with that of existing modified ratio estimators. Further we have also derived the conditions for which the proposed estimators perform better than the existing modified ratio estimators. The performances of the proposed estimators are also assessed with that of the existing estimators for certain natural populations. From the numerical study it is observed that the proposed modified ratio estimators perform better than the existing modified ratio estimators.
Efficient class of estimators for population median using auxiliary information  [PDF]
Prayas Sharma,Rajesh Singh
Statistics , 2014,
Abstract: This article suggests an efficient class of estimators of population median of the study variable using an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator has been investigated along with its approximate mean square error. We have shown that proposed class of estimator is more efficient than estimator considered by Srivastava (1967), Gross (1980), Kuk and Mak (1989) Singh et al. (2003b), Al and Chingi (2009) and Singh and Solanki (2013). In addition theoretical findings are supported by an empirical study based on two populations to show the superiority of the constructed estimators over others.
MEAN–VARIANCE–SKEWNESS–KURTOSIS APPROACH TO PORTFOLIO OPTIM ZATION: AN APPLICATION IN ISTANBUL STOCK EXCHANGE
Burcu ARACIO?LU,Fatma DEM?RCAN,Haluk SOYUER
Ege Academic Review , 2011,
Abstract: Portfolio optimization, the construction of the best combination of investment instruments that will meet the investors’ basic expectations under certain limitations, has an important place in the finance world. In the portfolio optimization, the Mean Variance model of Mar-kowitz (1952) that expresses a tradeoff between return and risk for a set of portfolios, has played a critical role and affected other studies in this area. In the Mean Variance model, only the covariances between securi-ties are considered in determining the risk of portfolios. The model is based on the assumptions that investors have a quadratic utility function and the return of the securities is distributed normally. Various studies that investigate the validity of these assumptions find evidence against them. Asset returns have significant skewness and kurtosis. In the light of these findings, it is seen that in recent years researchers use higher order of moments in the portfolio selection (Konno et al, 1993; Chunhachinda et al, 1997; Liu et al, 2003; Harvey et al, 2004; Jondeau and Rockinger, 2006; Lai et al, 2006; Jana et al, 2007; Maringer and Parpas, 2009; Briec et al, 2007; Taylan and Tatl dil, 2010).In this study, in the mean- variance- skewness- kurtosis framework, multiple conflicting and competing portfolio objectives such as maximizing expected return and skewness and minimizing risk and kurtosis simultaneously, will be addressed by construction of a poly-nomial goal programming (PGP) model. The PGP model will be tested on Istanbul Stock Exchange (ISE) 30 stocks. Previous empirical results indicate that for all investor preferences and stock indices, the PGP approach is highly effective in order to solve the multi conflicting portfolio goals in the mean – variance - skewness – kurtosis frame-work. In this study, portfolios will be formed in accordance with the investor preferences over incorporation of higher moments. The ef-fects of preferences both on the combination of stocks in the port-folios and descriptive statistics of portfolio returns will be analyzed. Another aim of this study is to investigate the impacts of the incor-poration of skewness and kurtosis of asset returns into the portfolio optimization on portfolios’ returns descriptive statistics
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