On the Dynamic Cumulative Past Quantile Entropy Ordering

In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models.

A New Class of Life Distributions Based on Moment Inequalities

In this paper, a new class of life distribution is named new better than renewal used in moment generating function (NBRUmgf). A new test for exponentiality versus NBRUmgf based on moment inequalities is established. Pitman's asymptotic efficiencies, powers and critical values of the new test are calculated to assess the performance of the test. The right censored data is handled also. Finally some applications are applied to the new test.

On classes of life distributions based on the mean time to failure function

The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Genome-wide analysis of lncRNA stability in human

Transcript stability is associated with many biological processes, and the factors affecting mRNA stability have been extensively studied. However, little is known about the features related to human long noncoding RNA (lncRNA) stability. By inhibiting transcription and collecting samples in 10 time points, genome-wide RNA-seq studies was performed in human lung adenocarcinoma cells (A549) and RNA half-life datasets were constructed. The following observations were obtained. First, the half-life distributions of both lncRNAs and messanger RNAs (mRNAs) with one exon (lnc-human1 and m-human1) were significantly different from those of both lncRNAs and mRNAs with more than one exon (lnc-human2 and m-human2). Furthermore, some factors such as full-length transcript secondary structures played a contrary role in lnc-human1 and m-human2. Second, through the half-life comparisons of nucleus- and cytoplasm-specific and common lncRNAs and mRNAs, lncRNAs (mRNAs) in the nucleus were found to be less stable than those in the cytoplasm, which was derived from transcripts themselves rather than cellular location. Third, kmers-based protein−RNA or RNA−RNA interactions promoted lncRNA stability from lnc-human1 and decreased mRNA stability from m-human2 with high probability. Finally, through applying deep learning−based regression, a non-linear relationship was found to exist between the half-lives of lncRNAs (mRNAs) and related factors. The present study established lncRNA and mRNA half-life regulation networks in the A549 cell line and shed new light on the degradation behaviors of both lncRNAs and mRNAs.

A New Family of Extended Lindley Models: Properties, Estimation and Applications

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.