Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models

We continue the investigation of coupled Sachdev-Ye-Kitaev (SYK) models without Schwarzian action dominance. Like the original SYK, at large N and low energies these models have an approximate reparametrization symmetry. However, the dominant action for reparametrizations is non-local due to the presence of irrelevant local operator with small conformal dimension. We semi-analytically study different thermodynamic properties and the 4-point function and demonstrate that they significantly differ from the Schwarzian prediction. However, the residual entropy and maximal chaos exponent are the same as in Majorana SYK. We also discuss chain models and finite N corrections.

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

A Probability Mass Function for Various Shapes of the Failure Rates, Asymmetric and Dispersed Data with Applications to Coronavirus and Kidney Dysmorphogenesis

In this article, a discrete analogue of an extension to a two-parameter half-logistic model is proposed for modeling count data. The probability mass function of the new model can be expressed as a mixture representation of a geometric model. Some of its statistical properties, including hazard rate function, moments, moment generating function, conditional moments, stress-strength analysis, residual entropy, cumulative residual entropy and order statistics with its moments, are derived. It is found that the new distribution can be utilized to model positive skewed data, and it can be used for analyzing equi- and over-dispersed data. Furthermore, the hazard rate function can be either decreasing, increasing or bathtub. The parameter estimation through the classical point of view has been performed using the method of maximum likelihood. A detailed simulation study is carried out to examine the outcomes of the estimators. Finally, two distinctive real data sets are analyzed to prove the flexibility of the proposed discrete distribution.

Determination of Diagnostic Parameters of Power Plants Based on Internal Combustion Engines

The presented article shows a method for finding monitored parameters for creating a diagnostic system for autonomous power sources based on spark ignition engines and diesel engines. The classification of structures of autonomous power sources based on internal combustion engines has been carried out. The analysis of the design features of the most common back-up power sources on the market based on internal combustion engines (ICE) indicates the widespread use of generators with a synchronous alternator. The analysis of the design features of autonomous power supplies has made it possible to develop logical models for different designs. The influence of the occurrence of a faulty state of each element on other elements of the systems is analyzed, and the results of the analysis are summarized in tables. An informative Claude Chenon criterion is proposed for finding the optimal number of diagnostic parameters among an infinite number of possible combinations of physical parameters that characterize the system. When solving the problem, a hypothesis was proposed about the equiprobability of cases of exit from the working state of each of the elements of the system. The use of Claude Chenon allows you to find the parts that make up the generators, which with maximum efficiency reduce the degree of uncertainty in the system. After determining the residual entropy, the parts of the system are selected, the state of which should be monitored by the diagnostic system. For such parts of the system, diagnostic parameters are found and methods for obtaining them are indicated.

A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

Fractional Entropy-Based Test of Uniformity with Power Comparisons

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.