𝑯𝑵- Entropy: A New Measureof Information And Its Properties

Entropy measures the amount of uncertainty and dispersion of an unknown or random quantity, this concept introduced at first by Shannon (1948), it is important for studies in many areas. Like, information theory: entropy measures the amount of information in each message received, physics: entropy is the basic concept that measures the disorder of the thermodynamical system, and others. Then, in this paper, we introduce an alternative measure of entropy, called 𝐻𝑁- entropy, unlike Shannon entropy, this proposed measure of order α and β is more flexible than Shannon. Then, the cumulative residual 𝐻𝑁- entropy, cumulative 𝐻𝑁- entropy, and weighted version have been introduced. Finally, comparison between Shannon entropy and 𝐻𝑁- entropy and numerical results have been introduced.

Measures of Extropy for Concomitants of Generalized Order Statistics in Morgenstern Family

In this paper, a measure of extropy is obtained for concomitants of m-generalized order statistics in the Morgenstern family. The cumulative residual extropy (CREX) and negative cumulative extropy (NCEX) are presented for the rth concomitant of m-generalized order statistics. In addition, the problem of estimating the CREX and NCEX is studied utilizing the empirical method in concomitants of m-generalized order statistics. Some applications of these results are given for the concomitants of order statistics and record values.

Water Budget Closure in the Upper Chao Phraya River Basin, Thailand Using Multisource Data

Accurate quantification of the terrestrial water cycle relies on combinations of multisource datasets. This analysis uses data from remotely sensed, in-situ, and reanalysis records to quantify the terrestrial water budget/balance and component uncertainties in the upper Chao Phraya River Basin from May 2002 to April 2020. Three closure techniques are applied to merge independent records of water budget components, creating up to 72 probabilistic realizations of the monthly water budget for the upper Chao Phraya River Basin. An artificial neural network (ANN) model is used to gap-fill data in and between GRACE and GRACE-FO-based terrestrial water storage anomalies. The ANN model performed well with r ≥ 0.95, NRMSE = 0.24 − 0.37, and NSE ≥ 0.89 during the calibration and validation phases. The cumulative residual error in the water budget ensemble mean accounts for ~15% of the ensemble mean for both the precipitation and evapotranspiration. An increasing trend of 0.03 mm month−1 in the residual errors may be partially attributable to increases in human activity and the relative redistribution of biases among other water budget variables. All three closure techniques show similar directions of constraints (i.e., wet or dry bias) in water budget variables with slightly different magnitudes. Our quantification of water budget residual errors may help benchmark regional hydroclimate models for understanding the past, present, and future status of water budget components and effectively manage regional water resources, especially during hydroclimate extremes.

Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

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.

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.