Search

Мы изучаем инвариантные относительно перестановок случайные разбиения, основанные на базовом субординаторе Дикмана и соответствующем семействе распределений Пуассона-Дирихле. Показано, что распределение большой выборки вектора, представляющего размеры блоков и количество блоков в разбиении $\{1,2,…,n\}$ после нормирования и центрирования, является произведением независимых пуассоновских и нормального распределений. В ситуации с выборкой генов эти величины представляют обилие и количество генов, наблюдаемых в выборке размером $n$ из соответствующего распределения Пуассона-Дирихле. В этом контексте мы включаем краткое изложение известных результатов сходимости, касающихся субординатора Дикмана.

We calculate finite sample and asymptotic distributions for the largest censored and uncensored survival times, and some related statistics, from a sample of survival data generated according to an iid censoring model. These statistics are important for assessing whether there is sufficient followup in the sample to be confident of the presence of immune or cured individuals in the population. A key structural result obtained is that, conditional on the value of the largest uncensored survival time, and knowing the number of censored observations exceeding this time, the sample partitions into two independent subsamples, each subsample having the distribution of an iid sample of censored survival times, of reduced size, from truncated random variables. This result provides valuable insight into the construction of censored survival data, and facilitates the calculation of explicit finite sample formulae. We illustrate for distributions of statistics useful for testing for sufficient followup in a sample, and apply extreme value methods to derive asymptotic distributions for some of those., Comment: 34 pages, 9 figures

We derive the large-sample distribution of the number of species in a version of Kingman’s Poisson–Dirichlet model constructed from an $\alpha$ -stable subordinator but with an underlying negative binomial process instead of a Poisson process. Thus it depends on parameters $\alpha\in (0,1)$ from the subordinator and $r>0$ from the negative binomial process. The large-sample distribution of the number of species is derived as sample size $n\to\infty$ . An important component in the derivation is the introduction of a two-parameter version of the Dickman distribution, generalising the existing one-parameter version. Our analysis adds to the range of Poisson–Dirichlet-related distributions available for modeling purposes.

The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.

Reliable and unceasing exploitation of power electronic converters plays a major part in numerous applications. The aging effects on the performance of a dc–dc boost power converter with different thermal structures are under consideration in this study. This article demonstrates the feasibility of using sensitivity analysis for a much more accurate estimation of the power converters’ performances. This article deals with a dc–dc boost converter as a case study in two thermal structures (coupled and decoupled) for electric vehicle application. Significant self and reciprocal effects of components can immensely affect the reliability assessment in thermal coupled structures. It reveals that the useful lifetime of the insulated-gate bipolar transistor (IGBT) and the diode can decrease by 35% and 44%, respectively. In thermal decoupled structures, there are no significant reciprocal effects either in electrical or thermal operating points (EOP/TOP). The results reveal the importance of reciprocal aging and self-aging effects on the reliability assessment in coupled thermal structures.

The $$\text {PD}_\alpha ^{(r)}$$ distribution, a two-parameter distribution for random vectors on the infinite simplex, generalises the $$\text {PD}_\alpha $$ distribution introduced by Kingman, to which it reduces when $$r=0$$ . The parameter $$\alpha \in (0,1)$$ arises from its construction based on ratios of ordered jumps of an $$\alpha $$ -stable subordinator, and the parameter $$r>0$$ signifies its connection with an underlying negative binomial process. Herein, it is shown that other distributions on the simplex, including the Poisson–Dirichlet distribution $$\text {PD}(\theta )$$ , occur as limiting cases of $$\text {PD}_\alpha ^{(r)}$$ , as $$r\rightarrow \infty $$ . As a result, a variety of connections with species and gene sampling models, and many other areas of probability and statistics, are made.

Today, with improvements in industrial methods, many products are designed to function for a long time before they fail. Since failure data play an important role in assessing the reliability of products, some alternative ways need to be found. Collecting degradation data can provide useful information in such cases. Using stochastic processes to model degradation data is common. Due to its favorable properties in this respect, inverse Gaussian process has attracted a lot of attention recently. In this paper, at first a constant-stress accelerated degradation test is planned when the degradation path follows the inverse Gaussian process and then the corresponding optimal design is obtained. To reach this aim, we employ the D-optimality criterion and prove that the optimal CSADT plan with multiple stress levels degenerates to two-stress-level test plans only using the minimum and maximum stress levels under model assumptions. Then, the optimal sample allocation for each stress level is obtained and the effect of stress levels on the objective function is determined. Finally, a real example and simulation studies are presented for more illustration.

We consider a random self-similar polynomials where the coefficients form a sequence of independent normally distributed random variables. We study the behavior of the expected density of real zeros of these polynomials when the variances of the middle coefficients are substantially larger than the others. Numerical sets show the existence of a phase transition for a critical value of a parameter that defines the variance. We also discuss the case where the variances of the coefficients are decreasing, and obtain the asymptotic behavior of the expected number of real zeros of such polynomials.

Recently, a step-stress accelerated degradation test plan, in which the stress level is elevated when the degradation value of a product crosses a prespecified value, was proposed. The times of stress level elevating are random and vary from product to product. In this paper, we extend this model to a more economic plan. The proposed extended model has two economical advantages compared with the previous one. The first is that the times of stress level elevating in the new model are identical for all products, which enable us to use only one chamber (oven) for testing all test units. The second is that, the new method does not require continuous inspection and to elevate the stress level, it is not necessary for the experimenter to inspect the value of the degradation continually. The new method decreases the cost of measurement, and also there is no need to use electronic sensors to detect the first passage time of the degradation to the threshold value in the new method. We assume that the degradation path follows a gamma process. The stress level is elevated as soon as the measurement of the degradation of one of the test units, at one of the specified times, exceeds the threshold value. Under the constraint that the total experimental cost does not exceed a prespecified budget, the optimal settings including the optimal threshold value, sample size, measurement frequency, and termination time are obtained by minimizing the asymptotic variance of an estimated quantile of the lifetime distribution of the product. A case study is presented to illustrate the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

In this article, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this article. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distrib...

A model is presented in this article based on a bivariate gamma process in which, the first component is latent and determines the failure time and the second represents the marker. This process is a more realistic model for a degradation process. After introducing the model, we obtain failure and survival probability distributions and discuss parametric and predictive inferences based on the Maximum Likelihood method and in a Bayesian setup.

A Profile Hidden Markov Model (PHMM) is a standard form of a Hidden Markov Models used for modeling protein and DNA sequence families based on multiple alignment. In this paper, we implement Baum-Welch algorithm and the Bayesian Monte Carlo Markov Chain (BMCMC) method for estimating parameters of small artificial PHMM. In order to improve the prediction accuracy of the estimation of the parameters of the PHMM, we classify the training data using the weighted values of sequences in the PHMM then apply an algorithm for estimating parameters of the PHMM. The results show that the BMCMC method performs better than the Maximum Likelihood estimation.