نشریه اندیشه آماری
سال بیست و سوم شماره 2 (پیاپی 46، پاییز و زمستان 1397)

‎In this paper‎, ‎a new distribution is introduced‎, ‎which is a generalization of a well-known distribution‎. ‎This distribution is flexible and applies to income data modeling‎. ‎We first provide some of the mathematical and distributional properties of this new model and then‎, ‎to demonstrate the flexibility the new distribution‎, ‎we will present the applications of this distribution with real data‎. ‎Data fitting results confirm the appropriateness of this new model for the real data set‎.

‎In this paper‎, ‎a new estimate of exponential type of auxiliary information to help simple random sampling without replacement of the finite population mean is introduced‎. ‎This new estimator with a few other estimates using two real data sets are compared with the mean square error‎.

‎Cardiovascular diseases (CVDs) are the leading cause of death worldwide‎. ‎To specify an appropriate model to determine the risk of CVD and predict survival rate‎, ‎users are required to specify a functional form which relates the outcome variables to the input ones‎. ‎In this paper‎, ‎we proposed a dimension reduction method using a general model‎, ‎which includes many widely used survival models as special cases‎.


‎Using an appropriate combination of dimension reduction and Cox Proportional Hazards model‎, ‎we found a method which is effective for survival prediction‎.

‎WinBUGS is one of the usual softwares in computational Bayesian statistics‎, ‎which is used to fit Baysian models easily‎. ‎Although this software has usual mathematical functions and statistical distributions as built in functions‎, ‎sometimes it is necessary to include other functions and distributions in computations which is done by some tricks and indirectly‎. ‎By using WinBUGS development interface (known as WBDev)‎, ‎new mathematical functions and statistical distributions can be added in the software‎. ‎This method facilitates writing codes of statistical models‎, ‎increases speed of computations and make computations more efficient‎. ‎In this paper‎, ‎the stages of including new mathematical functions and statistical distributions in the WinBUGS are illustrated by some examples‎.

‎Many point process models have been proposed for studying variety of scientific disciplines‎, ‎including geology‎, ‎medicin‎, ‎astronomy‎, ‎forestry‎, ‎ecology and ect‎. ‎The assessment of fitting these models is important‎. ‎Residuals-based methods are appropriate tools for evaluating good fit of spatial point of process models‎. ‎In this paper‎, ‎first‎, ‎the concepts related to the Voronoi residuals are investigated‎. ‎Then‎, ‎after fitting a cluster point process to the data set of the position of the trees in the Guilan forest‎, ‎the proposed model is evaluated using these residuals‎.

‎In this paper‎, ‎in order to establish a confidence interval (general and shortest) for quantiles of normal distribution in the case of one population‎, ‎we present a pivotal quantity that has non-central t distribution‎. ‎In the case of two independent normal populations‎, ‎we construct a confidence interval for the difference quantiles based on the generalized pivotal quantity and introduce a simple method for extracting its percentiles‎, ‎by which a shorter confidence interval can be constructed‎. ‎We will also examine the performance of the proposed methods by using simulations and examples‎.

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.

‎The purpose of this study was to determine and evaluate of spatial distribution of gold and silver elements concentration by using geostatistical methods‎. ‎This study was carried out in Ghezel Ozen area for 95 samples of lithogeochemicals‎. ‎At first‎, ‎Censor data was replaced and the values of outlier's data were identified using the box-Plot and Q-Q-Plot charts and reduced by the Doerffel method‎. ‎Finally‎, ‎the data were normalized using logarithmic transformations and then the geostatistical analysis was used‎. ‎Variogram studies showed that the spherical model is the best fitted model and the spatial correlation range for the two elements of Au and Ag were approximately 2500 m‎. ‎Finally‎, ‎the estimation and estimation variance maps of the studied elements were prepared by using ordinary kriging geostatistical method with the spherical model on the GS‎+ ‎software‎. ‎Evaluating the results by calculating the root mean square error (RMSE) and calculating the mean absolute error (MAE) indicates the acceptable accuracy of variogram model‎. ‎By studying the kriging estimation and kriging estimation variance maps‎, ‎the anomal regions were introduced for the elements of Au and Ag in the case study‎.

‎The censored data are widely used in statistical tests and parameters estimation‎. ‎In some cases e.g‎. ‎medical accidents which data are not recorded at the time of occurrence‎, ‎some methods such as interval censoring are used‎. ‎In this paper‎, ‎for a random sample uniformly distributed on the interval (0,θ) ‎the interval censoring have been used‎. ‎A consistent estimator of θ  and some asymptotically confidence intervals for θ are presented‎.

‎A simultaneous confidence band gives useful information on the reasonable range of the unknown regression model‎. ‎In this note‎, ‎when the predictor variables are constrained to a special ellipsoidal region‎, ‎hyperbolic and constant width confidence bonds for a multiple linear regression model are compared under the minimum volome confidence set (MVCS) criterion‎. ‎The size of one speical angle that determines the size of the predictor variable region is used to find out which band is better than the other‎. ‎When the angle and consquently the size of the predictor variable region is small‎, ‎the constant width band is better than the hyperbolic band‎.

‎When the angle hence the size of the predictor variable regoin is large‎, ‎the hyperbolic band is considerably better than the constant width band‎.