فهرست مطالب

Journal of Iranian Statistical Society
Volume:16 Issue: 2, 2017

  • تاریخ انتشار: 1396/08/22
  • تعداد عناوین: 6
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  • Reza Ývaliollahi, Akbar Asgharzadeh, Hon K. T. Ýng Pages 1-19
    ýLindley distribution has received considerable attention in the statistical literature due to its simplicityý. ýIn this paperý, ýwe consider the problem of predicting the failure times of experimental units that are censored in a right-censored experiment when the underlying lifetime is Lindley distributedý. ýThe maximum likelihood predictorý, ýthe best unbiased predictor and the conditional median predictor are derivedý. ýPrediction intervals based on these predictors are consideredý. ýWe further propose two resampling-based procedures for obtaining the prediction intervalsý. ýA numerical example is used to illustrate the methodology developed in this paperý. ýFinallyý, ýa Monte Carlo simulation study is employed to evaluate the performance of different prediction methodsý.
    Keywords: Bestý ýunbiased predictioný, ýConditional median predictioný, ýHighest conditional densityý, ýMaximum likelihood predictioný, ýPrediction interval
  • Malihe Mirali, Simin Baratpour Pages 21-32
    Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, Misagh et al. (2011) proposed a weighted information which is based on the cumulative entropy called Weighted Cumulative Entropy (WCE). The above-mentioned model is a Shiftdependent Uncertainty Measure. In this paper, we examine some of the properties of WCE and obtain some bounds for that. In order to estimate this information measure, we put forward empirical WCE. Furthermore, in some theorems, we have some characterization results. We explore that, if the WCE of the first (last) order statistic are equal for two distributions, then this two distributions will be equal.
    Keywords: Cumulative entropyý, ýCumulative residual entropyý, ýSurvival functioný, ýWeighted Shannon entropy
  • Mohammed Chowdhury, Ýlewis Vanbrackle, Mohammad Patwary Pages 33-50
    ýIn this articleý, ýwe develop two nonparametric smoothing estimators for parameter of a time-variant parametric modelý. ýThis parameter can be from any parametric family or from any parametric or semi-parametric regression modelý. ýEstimation is based on a two-step procedureý, ýin which we first get the raw estimate of the parameter at a set of disjoint time points and then compute the final estimator at any time by smoothing the raw estimatorsý. ýWe will call these estimators two-step local polynomial smoothing estimator and two-step kernel smoothing estimatorý. ýWe derive these two two-step smoothing estimators by modeling raw estimates of the time-variant parameter from any regression model or probability model and then establish a mathematical relationship between these two estimatorsý. ýOur two-step estimation method is applied to temperature data from Dhakaý, ýthe capital city of Bangladeshý. ýExtensive simulation studies under different cross-sectional and longitudinal frameworks have been conducted to check the finite sample MSE of our estimatorsý. ýNarrower bootstrap confidence bands and smaller MSEs from application and simulation results show the superiority of the local polynomial smoothing estimator over the kernel smoothing estimatorý.
    Keywords: Bandwidthý, ýKernel smoothingý, ýLocal polynomialsý, ýRaw estimatesý, ýTwo-step smoothing
  • Mehran Naghizadeh Qomi Pages 51-66
    ýThe problem of shrinkage testimation (test-estimation) for the Rayleigh scaleý ýparameter θ based on censored samples under the reflectedý ýgamma loss function is consideredý. We obtain the minimum riský ýestimator among a subclass and compute its riský. ýA shrinkageý ýtestimator based on acceptance or rejection of a null hypothesisý H0 : θ = θ0 is constructedý, ýwhere θ0 is a pointý ýguess value of θý. ýThe risk of the proposed shrinkageý ýtestimator is computed numerically and compared with the minimumý ýrisk estimatorý. ýA data set is analyzed for illustrativeý ýpurposesý. ý
    Keywords: Censored dataý, ýRayleigh distributioný, ýReflected gamma loss functionon
  • Anne Philip, P.Yageen Thomas Pages 67-95
    ýIn this paperý, ýwe have dealt with the distribution theory of concomitants of order statistics arising from Farlie-Gumbel-Morgenstern bivariate Lomax distributioný. ýWe have discussed the estimation of the parameters associated with the distribution of the variable Y of primary interestý, ýbased on the ranked set sample defined by ordering the marginal observations on an auxiliary variable Xý, ýwhen (X,Y) follows a Farlie-Gumbel-Morgenstern bivariate Lomax distributioný. ýWhen the association parameter and the shape parameter corresponding to Y are knowný, ýwe have proposed four estimatorsý, ýviz.ý, ýan unbiased estimator based on the Stoke's ranked set sampleý, ýthe best linear unbiased estimator based on the Stoke's ranked set sampleý, ýthe best linear unbiased estimator based on the extreme ranked set sample and the best linear unbiased estimator based on the multistage extreme ranked set sample for the scale parameter of the variable of primary interestý. ýThe relative efficiencies of these estimators have also been worked outý.
    Keywords: Best linear unbiased estimatorý, ýExtreme ranked set samplingý, ýFisher informationý, ýMultistage ranked set sampling
  • Kheirolah Okhli, Mahdieh Mozafari, Mehrdad Naderi Pages 97-110
    ýThis paper presents a new mixture model via considering the univariate skew Laplace distributioný. ýThe new model can handle both heavy tails and skewness and is multimodalý. ýDescribing some properties of the proposed modelý, ýwe present a feasible EM algorithm for iterativelyý ýcomputing maximum likelihood estimatesý. ýWe also derive the observed information matrix for obtainingý ýthe asymptotic standard error of parameter estimatesý. ýThe finite sample properties of the obtained estimatorsý ýas ýwell ýasý the consistency of the associated standard error of parameter estimates are investigated by aý ýsimulation studyý. ýWe also demonstrate the flexibility and usefulness of the new model by analyzing real dataý ýexampleý.
    Keywords: EM algorithm, Finite mixture model, Mean-variance mixture distribution, Skew Laplace distribution