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Here we present a novel inverse probability of censoring weighted (IPCW) adaptation of the Kochar–Gupta (KG) test of independence, in the case of bivariate randomly censored data. Three different censoring schemes are considered: one of the target variables is censored, both targeted variables are censored with the same censoring variable, and both target variables are censored with different censoring variables. The limiting properties of test statistics are explored. In order to compare the tests with a few well-known competitors in terms of powers, several resampling procedures have been utilised to approximate the null distribution. Special attention is dedicated to the comparison with a classical adaptation of the KG test related to the IPCW adaptation of U-statistics.

Recently, the characterization-based approach for the construction of goodness of fit tests has become popular. Most of the proposed tests have been designed for complete i.i.d. samples. Here, we present the adaptation of the recently proposed exponentiality tests based on equidistribution-type characterizations for the case of randomly censored data. Their asymptotic properties are provided. Besides, we present the results of wide empirical power study including the powers of several recent competitors. This study can be used as a benchmark for future tests proposed for this kind of data.

In this article we prove a generalization of the Ejsmont characterization (Ejsmont in Stat Probab Lett 114:1–5, 2016) of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the difference between the product of empirical characteristic functions and some constant. Special attention is given to the case of testing for univariate normality in which we derive the test statistic explicitly in terms of Bessel function and explore asymptotic properties. The simulation study also includes the cases of testing for bivariate and trivariate normality and independence, as well as multivariate normality. We show the quality performance of our test in comparison to some popular powerful competitors. The practical application of the proposed normality and independence test is discussed and illustrated using a real dataset.

We propose three new classes of goodness-of-fit tests for the Pareto type I distribution based on a characterization. The asymptotic null distribution for the tests are derived and their Bahadur efficiencies are compared to the efficiencies of some of the existing tests. It is found that the new integral type test has superior local efficiencies amongst the new tests, and in general, has higher efficiencies than the competing tests considered. The finite-sample performance of the newly proposed tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. It is found that the new tests (especially the integral type tests) perform favourably compared to the other tests.

The geometric distribution is one of the most widely used count distributions. Novel goodness of fit tests for this distribution are suggested taking advantage of a characterization of that distrib...

In this paper we estimate R = PfX < Yg when X and Y are independent random variables following the Peng-Yan extended Weibull distribution. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. In the case of equal shape parameters, we derive the exact confidence intervals, too. A procedure for deriving bootstrap-p confidence intervals is presented. The UMVUE of R and the UMVUE of its variance are derived and also the Bayes point and interval estimator of R for conjugate priors are obtained. Finally, we perform a simulation study in order to compare these estimators and provide a real data example.

We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L2-distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for many common alternatives, our tests perform better than the integral and Kolmogorov-type tests based on the same characterizations.

In this paper, we consider the problem of testing independence against stochastically increasing property. For the construction of new statistical tests, we employ Nadaraya–Watson regressio...

We study the Bahadur efficiency of several weighted L2--type goodness--of--fit tests based on the empirical characteristic function. The methods considered are for normality and exponentiality testing, and for testing goodness--of--fit to the logistic distribution. Our results are helpful in deciding which specific test a potential practitioner should apply. For the celebrated BHEP and energy tests for normality we obtain novel efficiency results, with some of them in the multivariate case, while in the case of the logistic distribution this is the first time that efficiencies are computed for any composite goodness--of--fit test.

We present new consistent goodness-of-fit tests for exponential distribution, based on the Desu characterization. The test statistics represent the weighted $L^2$ and $L^{\infty}$ distances between appropriate V-empirical Laplace transforms of random variables that appear in the characterization. In addition, we perform an extensive comparison of Bahadur efficiencies of different recent and classical exponentiality tests. We also present the empirical powers of new tests.

In this article, a new class of uniformity tests is proposed. It is shown that those tests are applicable to the cases of any simple null hypothesis as well as for the composite null hypothesis of ...

In this paper, the estimation of the stress-strength probability in a multicomponent model, in the case when all components follow the geometric distribution, is studied. This is the first time that multicomponent models with discrete probability distributions are considered. The MLE, UMVUE and Bayes point estimator, as well as asymptotic and bootstrap confidence intervals are presented. A simulation study is performed in order to compare the performance of various estimators. Finally, the methods are applied to real data examples from climatology and sport.

This paper proposes and studies two new classes of tests for exponentiality. Both of them are based on Basu's characterization of the exponential distribution. The null distributions of the test statistics are parameter free. Moreover, conveniently normalized, they are asymptotically normally distributed. The large sample behaviour of the proposed tests is studied for fixed alternatives, and for local alternatives by means of the approximate local Bahadur efficiency. The finite sample performance of the new tests is studied via simulation. Two of the new tests present a very high relative local Bahadur efficiency and a competing behaviour against fixed alternatives in relation to existing tests.

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems., Comment: Revised proof of Theorem 1; other minor changes in text

In this paper, some recent and classical tests of symmetry are modified for the case of an unknown centre. The unknown centre is estimated with its α-trimmed mean estimator. The asymptotic ...

Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are explored. The maximal eigenvalue, needed for the derivation of their logarithmic tail behavior, was calculated or approximated using techniques from the theory of linear operators and the perturbation theory. The quality of the tests is assessed using the approximate Bahadur efficiency as well as the simulated powers. The tests are shown to be comparable with some recent and classical tests of symmetry.

We propose specification tests for the innovation distribution in conditional duration models. The new tests are based either on the cumulative distribution function, or on exponential transforms such as the Laplace transform and the characteristic function, or on characterizations of the innovation-distribution under test. We study the finite-sample performance of the proposed procedures in comparison with alternative tests which employ nonparametric density estimates as well as with tests based on entropy. A bootstrap version of the tests is utilized in order to study the small sample behavior of the procedures. A real-data example illustrates the applicability of our method and confirms conclusions drawn by earlier authors.

A new characterization of symmetric distributions is presented. Two classes of distribution-free symmetry tests based on it are proposed. Their Bahadur efficiency is calculated and used for comparison with similar tests. Some classes of most favorable alternatives are also determined.

In this paper, a new class of goodness of fit tests for exponential distribution is proposed. The tests use the equidistribution characterizations of exponential distribution. Based on the U-empirical Laplace transforms of equidistributed statistics, test statistics of the integral type are formed. They are U-statistics with estimated parameters. Their asymptotic properties are derived. Two families of exponentiality tests from this class, based on two selected characterizations, are presented. The approximate Bahadur efficiency is used to assess their quality. Finally, their simulated powers are calculated and the tests are compared with different exponentiality tests.

We propose new exponentiality tests based on a recent characterization. We construct integral and Kolmogorov-type statistics, derive their asymptotics and calculate the Bahadur efficiency against some common alternatives. We also obtain a class of locally optimal alternatives for each test. In case of small samples tests are compared with some common exponentiality tests.

A wide set of recent and classical symmetry tests is compared in terms of empirical power against some flexible skew-symmetric alternatives. The comparison is done for i.i.d. data, as well as for linear and GARCH time series models. In addition, the tests are analyzed in terms of computational efficiency. The role of distribution-free tests that avoid time-consuming resampling techniques for determining empirical powers and p-values is pointed out. An asymptotic equivalence of test statistics in the i.i.d. and GARCH models is discussed for a class of distribution-free tests.

Polyphony, as a composing technique, has the same function in every historicallyartistic period – the development and enrichment of melodic lines. What distinguishes polyphony treatment throughout the epochs is the different sound impression of the stylistic musical period in which the composition was created. Musical language of choreographed scenes in Mirska pjenija by the composer Srdjan Jaćimović is to a large extent the musical language of our epoch, a language of postmodern orientation. The piece abounds with the impressionistic presentation of the atmosphere through musical expressing of the text. A detailed polyphonic analysis of the composition indicates the use of different types of polyphony in each of the choreographed scenes individually, which are systematically separated and explained in this paper.

Two families of scale-free exponentiality tests based on the recent characterization of exponentiality by Arnold and Villasenor are proposed. The test statistics are constructed using suitable functionals of U -empirical distribution functions. The family of integral statistics can be reduced to V - or U -statistics with relatively simple non-degenerate kernels. They are asymptotically normal and have reasonably high local Bahadur efficiency under common alternatives. This efficiency is compared with simulated powers of new tests. On the other hand, the Kolmogorov type tests demonstrate very low local Bahadur efficiency and rather moderate power for common alternatives, and can hardly be recommended to practitioners. The conditions of local asymptotic optimality of new tests are also explored and for both families special "most favourable" alternatives for which the tests are fully efficient are described.

Two new tests for exponentiality, of integral- and Kolmogorov-type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.

Previous year has been everything but peaceful considering the Arab world. Some of the Middle Eastern and North African countries had a year full of political and military problems followed usually with people's demonstrations and regime fallings in the end. The thing that in a way had a very tight connection with these instabilities were social networks. This paper is mostly focused on the idea of social networks as a leading engine for making these revolutions possible. If we look at the social network characteristics and all of the things that make them suitable for this kind of tool for a society democratization, it is obvious why the story about Facebook and Twitter in the Arab spring had that kind of a world impact. Even though these stories made these social platforms inevitable when talking about last year's revolutions, it is necessary to make a distance in analysing them. It is important to underline their impact in making revolution as big as it was specially its impact on the western public. On the other hand bigger part of western media made these networks something much bigger than they could be - the revolution itself, or the mean for regime fighting without which Arab spring wouldn't even be this important. The biggest and most important role of Facebook, Twitter and all the others was to change minds and power perception, to inform people about the things that were happening on the streets in countries of Arab world and to make possible massive mobilization of people and their attention. This is why social networks are just starting to open their way towards some new roles and functions that we probably could not even dreamt about.

In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for goodness-of-fit testing. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case.

In this paper some new characterizing theorems of the exponential distribution based on the order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.

In this paper we present a new characterization of Pareto distribution and consider goodness of fit tests based on it. We provide an integral and Kolmogorov- Smirnov type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes we compare the power of those tests with some common goodness of fit tests., Accepted for publication in "Statistics"

In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its variance are derived and also the Bayes estimator of R for conjugate prior distributions is obtained. Finally, we perform a simulation study in order to compare these estimators. keywords: stress-strength, geometric distribution, Poisson distribution, maximum likelihood estimator, Bayes estimator, UMVUE, bootstrap confidence intervals. MSC(2010): 62F10, 62F12, 62F15, 62F25, 62F40.

In reliability theory, one of the main problems is estimating parameter \(R = P\{X < Y\}\). In this paper we shall present UMVUEs for \(R\) in different cases i.e. for different distributions of \(X\) and \(Y\). Some of them are already existing and some are original.