In this paper, when the stress and strength are two independent Kumaraswamy random variables, we derive the point and interval estimate of the stress-strength parameter, from both frequentist and Bayesian viewpoints, under the Type-II hybrid progressive censoring scheme. In fact, the problem is solved in two cases. First, with the assumption that the stress and strength have different first shape parameters and the common second shape parameter, we attain maximum likelihood estimate (MLE), approximation MLE, and two Bayesian approximation estimates, Lindley's approximation and the Markov chain Monte Carlo (MCMC) method, due to lack of closed forms. Also, the asymptotic confidence interval of R is constructed by asymptotic distribution of it. Moreover, by using the MCMC method, we achieve the highest posterior density credible intervals. Second, with the assumption that the common shape parameter is known, we attain the MLE, the exact Bayes estimate, and the uniformly minimum-variance unbiased estimate of R. Also, we construct the asymptotic and Bayesian intervals for the stress-strength parameter. Furthermore, to compare the performance of various methods, we apply the Monte Carlo simulation. Finally, one real dataset is analyzed for demonstrative aims.

In reliability engineering, the Weibull distribution and censoring are widely employed. The multiple Type-I censoring is the general form of Type-I censoring and represents that all the test units are terminated at different times. In this paper, the exact inference on Weibull parameters under multiple Type-I censoring is discussed, as the existing studies are limited. The least-square estimates (LSE) and maximum likelihood estimates (MLE) of Weibull parameters are presented. For the problem that the MLE does not always exist and has no closed-form, the approximate maximum likelihood estimate (AMLE) is proposed. Concerning the confidence interval (CI) for Weibull parameters, the pivotal quantity based on the LSE is developed to construct it. Another CI is obtained using the asymptotic normality of MLE. By the missing information principle, the observed Fisher information matrix is derived to replace the commonly approximate one through evaluating the second order derivatives of log-likelihood function with the MLE. As a comparison, the CI via the bootstrap method is provided. Monte Carlo simulation demonstrates that the proposed AMLE is convenient and superior to the MLE. And the proposed CI based on pivotal quantity outperforms others. Besides, the derived observed Fisher information matrix is also better. Finally, a real example is analyzed to illustrate the application of proposed methods.

We point out that the beta hazard rate distribution introduced by Lai and Jones is a particular case of Libby and Novick's beta distribution known since 1982.

A three-parameter discrete distribution is introduced based on a recent modification of the continuous Weibull distribution. It is one of only three discrete distributions allowing for bathtub shaped hazard rate functions. We study some of its mathematical properties, discuss estimation by the method of maximum likelihood, and describe applications to four real data sets. The new distribution is shown to outperform at least three other models including those allowing for bathtub shaped hazard rate functions.

MOTIVATION: As an epigenetic alteration, DNA methylation plays an important role in epigenetic controls of gene transcription. Recent advances in genome-wide scan of DNA methylation provide great opportunities in studying the impact of DNA methylation on many human diseases including various types of cancer. Due to the unique feature of this type of data, applicable statistical methods are limited and new sophisticated approaches are desirable. RESULTS: In this article, we propose a new statistical test to detect differentially methylated loci for case control methylation data generated by Illumina arrays. This new method utilizes the important finding that DNA methylation is highly correlated with age. The proposed method estimates the overall P-value by combining the P-values from independent individual tests each for one age group. Through real data application and simulation study, we show that the proposed test is robust and usually more powerful than other methods.

An explicit expression is derived for the selection intensity of genetic algorithms discussed by Ahn and Ramakrishna, 2003. The expression involves a well-known special function. The practical issues of using the expression (including a simple approximation) are discussed.

In the recent paper by Cetinkaya et al , admission control tests are derived by approximating the sum of two Gumbel distributed random variables by a Gumbel distributed random variable. In fact, the sum of two Gumbel distributed random variables does not follow a Gumbel distribution. Here, explicit expressions are derived for the probability density function (pdf) and the cumulative distribution function (cdf) of the exact distribution of the sum. The discrepancy between the exact and the approximate distributions is studied numerically.

It is pointed out that the two beta-type distributions introduced by Tardon et al. have been known before in the statistics literature.

Maximum and minimum of correlated Gaussian random variables arise naturally with respect to statistical static time analysis. It appears, however, that only approximations have been used in the literature to study the distribution of the max/min of correlated Gaussian random variables. In this paper, we would like to point out that the statistics literature has long established simple expressions for the exact distribution of the max/min. We provide some of the known expressions for the following: the probability density function, moment generating function, and the moments. We also provide two simple programs for computing the probability density functions of the max/min and an illustration of the results to statistical static time analysis.

A closed form expression is derived for the moment generating function of the output decision variable considered by Shi and Latva-Aho (2005).

Abstract The bit error probability (BEP) for many wireless communications networks can be expressed in the form R = Pr (X2 < X1) where X1 and X2 are independent random variables. Here, a comprehensive collection of formulas is derived for R by assuming the most commonly known models for X1 and X2. A discussion is provided of four possible applications to problems in wireless communications. Copyright © 2007 John Wiley & Sons, Ltd.

The recent paper by Abdelfattah and Nicolas proposed a novel coherence magnitude estimator and studied its properties. Here, we derive simpler and more explicit expressions for four of the properties that were studied: 1) the probability density function; 2) moments; 3) Mellin transform; and 4) second-kind moments. We establish numerical efficiency of these expressions and provide simple Maple programs for inversion. We expect that the results presented here could enhance applicability of the new estimator.

Performance analysis of the normalized adaptive matched filter (NAMF) operating in homogeneous Gaussian clutter has received considerable attention in the recent years (see ). In this letter, for the first time, exact and explicit expressions are derived for the associated probability of false alarm and the probability of detection. The practical advantages of using the derived expressions are established.

Simpler forms are derived for the properties of trivariate and quadrivariate Rayleigh distributions considered by Chen and Tellambura

Closed-form expressions are derived for the minimum duration outage and the probability of outage considered by Lai and Mandayam in the above paper.

A closed-form expression is derived for the moment generating function of the Weibull distribution when its shape parameter is a rational number.

For original paper, see Nikolaidis and Pitas (IEEE Trans. Image Process., vol.12, no.5, p.563-71, May 2003). Explicit expressions are derived for the Fisher information for the generalized Gaussian noise model considered by Nikolaidis and Pitas

An explicit analytical expression is derived for computing the expected number of symmetric neighbors considered by Huang and Shen [1]. The expression involves a well-known special function. The practical advantages of using the analytical expression are established.

Corrections to (6) in "A simple procedure for Bayesian estimation of the Weibull distribution" (vol. 54, pp. 612-616, Dec 05) are presented here.

The distributions of linear combinations, and ratios of random variables arise explicitly in many reliability problems. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this paper, the exact distributions of alphaX+betaY, and X/Y are derived when X, and Y follow two of the most applied models in reliability. Computer programs for calculating the associated percentage points are also given

Gierull provides a statistical analysis of multilook synthetic aperture radar interferograms. Various expressions for the probability density function, cumulative distribution function, and the moments of associated statistics are derived. It appears, however, that most of these expressions are based on some approximation. In this letter, the corresponding expressions are derived in their exact form, including some elementary representations for certain expressions given by Gierull. A numerical comparison of the exact and approximate expressions is provided

Explicit expressions are derived for the cumulants and the cumulant-generating function of the log-transformed radar cross section considered by Solbo and Eltoft. Some computational issues are also discussed

Explicit expressions are derived for the actual discrete cosine transform (DCT) coefficient distribution. Associated estimation procedures are also derived for ready use in practical applications

The multivariate survival function of a random vector X is used to define a broad class of entropy measures. Several properties of the proposed class are studied and explicit expressions of the measures derived for specific probabilistic models. The cumulative residual entropy, introduced by Rao et al. and Wang et al., is a particular case of the proposed class of measures.

Since the turn of the century, several papers have appeared in reliability journals (including the IEEE Transactions on Reliability) which claim to have proposed new modifications of the traditional Weibull distribution. It is pointed out here that the proposed distributions are either not new, or arise from a representation suggested by Gurvich et al. . A modification is suggested that contains all of the proposed distributions as particular cases.