فهرست مطالب

  • Volume:17 Issue: 2, 2018
  • تاریخ انتشار: 1397/09/10
  • تعداد عناوین: 10
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  • B.L.S‎. ‎ Prakasa Rao* Pages 1-12

    ‎As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90)‎, ‎we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185)‎. ‎We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censored data‎.

    Keywords: Cauchy-Schwartz inequality, Cramer-Rao inequality, Randomly censored data, Walker's inequality‎
  • Siavash Pirzadeh Nahooji, Rahman Farnoosh*, Nader Nematollahi Pages 13-35

    ‎In this paper‎, ‎the nonlinear regression models when the model errors follow a slash‎ ‎skew-elliptical distribution‎, ‎are considered‎. ‎In the special case‎ ‎of nonlinear regression models under slash skew-t distribution‎, ‎we‎ ‎present some distributional properties‎, ‎and to estimate their‎ ‎parameters‎, ‎we use an EM-type algorithm‎. ‎Also‎, ‎to find the‎ ‎estimation errors‎, ‎we derive the observed information matrix‎ ‎analytically‎. ‎To describe the influence of the observations on the‎ ‎ML estimates‎, ‎we use a sensitivity analysis‎. ‎Finally‎, ‎we conduct‎ ‎some simulation studies and a real data analysis to show the‎ ‎performance of the proposed model‎.

    Keywords: EM algorithm, ‎Nonlinear regression, ‎Skew normal distribution, ‎Skew-t distribution, ‎Slash skew-elliptical distribution, ‎Slash skew-t distribution
  • Jeffrey S. Pai, Nalini Ravishanker* Pages 37-55

    ‎Pricing weather derivatives is becoming increasingly useful‎, ‎especially in developing economies‎. ‎We describe a statistical model based approach for pricing weather derivatives by modeling and forecasting daily average temperatures data which exhibits long-range dependence‎. ‎We pre-process the temperature data by filtering for seasonality and volatility and fit autoregressive fractionally integrated moving average (ARFIMA) models‎, ‎employing the preconditioned conjugate gradient (PCG) algorithm for fast computation of the likelihood function‎. ‎We illustrate our approach using daily temperatures data from 1970 to 2008 for cities traded on the Chicago Mercantile Exchange (CME)‎, ‎which we employ for pricing degree days futures contracts‎. ‎We compare the statistical approach with traditional burn analysis using a simple additive risk loading principle for pricing‎, ‎where‎ ‎the risk premium is estimated by the method of least squares using data on observed prices and the corresponding estimate of prices from the best model we fit to the temperatures data.

    Keywords: ARFIMA model‎, ‎Burn analysis‎, ‎Daily temperature‎, ‎Prediction
  • Fiaz Ahmad Bhatti*, G.G. Hamedani, Munir Ahmad Pages 57-89

    In this paper‎, ‎we present a modified Log Burr XII (MLBXII) distribution developed on the basis of a generalized log Pearson differential equation‎. ‎This distribution is also obtained from a compounding mixture of‎ ‎distributions‎. ‎Moments‎, ‎inequality measures‎, ‎uncertainty measures and reliability measures are theoretically established‎. ‎Characterizations of MLBXII distribution are also studied via different techniques‎. ‎Parameters of MLBXII distribution are‎ ‎estimated using the maximum likelihood method‎. ‎Goodness of fit of this distribution through different methods is studied.

    Keywords: Moments, Uncertainty, Reliability, Characterizations, Maximum Likelihood
  • Muhammad Umair Sohail*, Shabbir Javid, ‎Cem Kadilar, Shakeel Ahmed Pages 91-117

    ‎When there is a high correlation between the study and auxiliary variables‎, ‎the rank of the auxiliary variable also correlates with the study variable‎. ‎Then‎, ‎the use of the rank as an additional auxiliary variable may be helpful to increase the efficiency of the estimator of the mean or the total number of the population‎. ‎In the present study‎, ‎we propose two generalized families of estimators for imputing the scrambling responses by using the variance and the rank of the auxiliary variable‎. ‎Expressions for the bias and the mean squared error are obtained up to the first order of approximation‎. ‎A numerical study is carried out to observe the performance of estimators‎. ‎

    Keywords: Higher order moments‎, ‎Imputation‎, ‎Missing data‎, ‎Scrambled responses‎, ‎Sensitive attribute‎
  • Fatemeh Arezoomand, Masoud Yarmohammadi, Rahim Mahmoudvand* Pages 119-140

    The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution‎. ‎We present a detailed theoretical description of this distribution‎. ‎We try to estimate the parameters of AUL distribution using the maximum likelihood method‎. ‎Since the likelihood approach results in complicated forms‎, ‎we suggest a bootstrap-based approach for estimating the parameters‎. ‎The proposed method is mainly based on the shape of the empirical density‎. ‎We conduct a simulation study to assess the performance of the proposed procedure‎. ‎We also fit the AUL distribution to real data sets‎: ‎daily working time and Pontius data sets‎. ‎The results show that AUL distribution is a more appropriate choice than the Skew-Normal‎, ‎Skew t‎, ‎Asymmetric Laplace and Uniform-Normal distributions.

    Keywords: Estimation‎, ‎Fitting‎, ‎Uniform-Laplace distribution
  • Mehmet Yilmaz* Pages 141-164

    In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎ [-1,1] to [-1,k]‎. ‎At this point‎, ‎the generated distributions gain more‎ ‎ flexibility than a transmuted distribution constructed by QRTM‎. ‎The distribution family obtained in this transmutation is considered‎ to be an alternative to the distribution families obtained by quadratic rank‎ transmutation‎. ‎Statistical and reliability properties of this family are‎ examined‎. ‎Considering Weibull distribution as the base distribution‎, ‎the‎ importance and the flexibility of the proposed families are illustrated by two‎ applications‎.

    Keywords: Polynomial Rank Transmutation‎, ‎Quadratic Rank Transmutation‎, ‎Transmuted Distribution‎, ‎Transmuted-Weibull
  • Mehdi Omidi*, Mohsen Mohammadzadeh Pages 165-179

    ‎One of the most useful tools for handling multivariate distributions of dependent variables in terms of their marginal distribution is a copula function‎. ‎The copula families capture a fair amount of attention due to their applicability and flexibility in describing the non-Gaussian spatial dependent data‎. ‎The particular properties of the spatial copula are rarely seen in all the known copula families‎. ‎In the present paper‎, ‎based on‎ ‎the weighted geometric mean of two Max-id copulas family‎, ‎the spatial copula function is provided‎. ‎Afterwards‎, ‎the proposed copula‎ ‎along with the Bees algorithm is used to explore the spatial dependency and to interpolate the rainfall data in Iranchr('39')s Khuzestan province‎.

    Keywords: Spatial copula function, Random‎ ‎field, Max-id copulas
  • Hadi Emami* Pages 181-203

    In this article we consider the stochastic restricted ridge estimation in semiparametric linear models when the covariates are measured with additive errors‎. ‎The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates‎. ‎The asymptotic normality of the resulting estimates are established‎. ‎Also‎, ‎necessary and sufficient conditions‎, ‎for the superiority of the proposed estimator over its counterpart‎, ‎for selecting the ridge parameter k are obtained‎. ‎A Monte Carlo simulation study is also performed to illustrate the finite sample performance of the proposed procedures‎. ‎Finally theoretical results are applied to Egyptian pottery Industry data set.

    Keywords: Cross validation‎, ‎Measurement error‎, ‎Multicollinearity‎, ‎Semiparametric linear regression‎, ‎Shrinkage estimator
  • Vahid Rezaei Tabar*, Dariusz Plewczynski, Hosna Fathipor Pages 205-225

    The parameters of a Hidden Markov Model (HMM) are transition and emission probabilities‎. ‎Both can be estimated using the Baum-Welch algorithm‎. ‎The process of discovering the sequence of hidden states‎, ‎given the sequence of observations‎, ‎is performed by the Viterbi algorithm‎. ‎In both Baum-Welch and Viterbi algorithms‎, ‎it is assumed that‎, ‎given the states‎, ‎the observations are independent from each other‎. ‎In this paper‎, ‎we first consider the direct dependency between consecutive observations in the HMM‎, ‎and then use conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model for generalizing the Baum-Welch and Viterbi algorithms‎. ‎We compare the performance of the generalized algorithms with the commonly used ones in simulation studies for synthetic data‎. ‎We finally apply these algorithms on real data sets which are related to biological and inflation data‎. ‎We show that the generalized Baum-Welch and Viterbi algorithms significantly outperform the conventional ones when sample sizes become larger‎.

    Keywords: Baum-Welch Algorithm‎, ‎Bayesian Network‎, ‎Hidden Markov Model‎, ‎Viterbi Algorithm