Exponentiality test based on Renyi distance between equilibrium distributions

ABSTRACT

On the basis of Csiszar's φ-divergence discrimination information, we propose a measure of discrepancy between equilibriums associated with two distributions. Proving that a distribution can be characterized by associated equilibrium distribution, a Renyi distance of the equilibrium distributions is constructed that made us to propose an EDF-based goodness-of-fit test for exponential distribution. For comparing the performance of the proposed test, some well-known EDF-based tests and some entropy-based tests are considered. Based on the simulation results, the proposed test has better powers than those of competing entropy-based tests for the alternatives with decreasing hazard rate function. The use of the proposed test is evaluated in an illustrative example.     

NONPARAMETRIC TWO SAMPLE TESTS BASED ON AREA STATISTICS

ABSTRACT

Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper presents a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations, such as testing equality of distributions against inequality or testing stochastic dominance of distributions in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distributions of the statistics (under F=G) can be calculated via recursion formulae. Two tables with critical values of the new statistics are included. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian bridge. The distribution functions and quantiles thereof are obtained by Monte Carlo simulation. Finally, the power functions of the two new tests based on area statistics are compared to the power functions of the tests based on the corresponding supremum statistics, i.e., statistics of the Kolmogorov–Smirnov type.     

Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation

Box–Cox together with our newly proposed transformation were implemented in three different real world empirical problems to alleviate noisy and the volatility effect of them. Consequently, a new domain was constructed. Subsequently, universe of discourse for transformed data was established and an approach for calculating effective length of the intervals was then proposed. Considering the steps above, the initial forecasts were performed using frequently used fuzzy time series (FTS) methods on transformed data. Final forecasts were retrieved from initial forecasted values by proper inverse operation. Comparisons of the results demonstrate that the proposed method produced more accurate forecasts compared with existing FTS on original data.     

Discrete Linnik Weibull distribution

Abstract

We introduce a new family of distributions using truncated discrete Linnik distribution. This family is a rich family of distributions which includes many important families of distributions such as Marshall–Olkin family of distributions, family of distributions generated through truncated negative binomial distribution, family of distributions generated through truncated discrete Mittag–Leffler distribution etc. Some properties of the new family of distributions are derived. A particular case of the family, a five parameter generalization of Weibull distribution, namely discrete Linnik Weibull distribution is given special attention. This distribution is a generalization of many distributions, such as extended exponentiated Weibull, exponentiated Weibull, Weibull truncated negative binomial, generalized exponential truncated negative binomial, Marshall-Olkin extended Weibull, Marshall–Olkin generalized exponential, exponential truncated negative binomial, Marshall–Olkin exponential and generalized exponential. The shape properties, moments, median, distribution of order statistics, stochastic ordering and stress–strength properties of the new generalized Weibull distribution are derived. The unknown parameters of the distribution are estimated using maximum likelihood method. The discrete Linnik Weibull distribution is fitted to a survival time data set and it is shown that the distribution is more appropriate than other competitive models.     

Orientation relationship in finite dimensional space

In the present article, we discuss the regression of a point on the surface of a unit sphere in d dimensions given a point on the surface of a unit sphere in p dimensions, where p may not be equal to d. Point projection is added to the rotation and linear transformation for regression link function. The identifiability of the model is proved. Then, parameter estimation in this set up is discussed. Simulation studies and data analyses are done to illustrate the model.     

Comparison of Interval Estimators of Pr(X < Y) in the Two-parameter Exponential Distribution

We consider confidence intervals for the stress–strength reliability Pr(X< Y) in the two-parameter exponential distribution. We have derived the Bayesian highest posterior density interval using non-informative prior distributions. We have compared its performance with the intervals based on the generalized pivot variable intervals in terms of their coverage probabilities and expected lengths. Our simulation study shows that the Bayesian interval performs better according to the criteria used, especially when the sample sizes are very small. An example is given.     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

Temporal Disaggregation: Methods,Information Loss,and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.