Linear Regression Analysis

Studies stochastic models of queueing, reliability, inventory, and sequencing in which random influences are considered. One stochastic mode--rl is approximated by another that is simpler in structure or about which simpler assumptions can be made. After general results on comparison properties of random variables and stochastic processes are given, the properties are illustrated by application to various queueing models and questions in experimental design, renewal and reliability theory, PERT networks and branching processes.

https://link.springer.com/content/pdf/10.1057%2Fjors.1984.224.pdf

Comparison Methods for Queues and Other Stochastic Models

(2007). Stochastic Ageing and Dependence for Reliability. Technometrics: Vol. 49, No. 2, pp. 222-222.

Stochastic Ageing and Dependence for Reliability

With the quick development and popularity of computers, computer-generated signals have drastically invaded into our daily lives. Screen content image is a typical example, since it also includes graphic and textual images as components as compared with natural scene images which have been deeply explored, and thus screen content image has posed novel challenges to current researches, such as compression, transmission, display, quality assessment, and more. In this paper, we focus our attention on evaluating the quality of screen content images based on the analysis of structural variation, which is caused by compression, transmission, and more. We classify structures into global and local structures, which correspond to basic and detailed perceptions of humans, respectively. The characteristics of graphic and textual images, e.g., limited color variations, and the human visual system are taken into consideration. Based on these concerns, we systematically combine the measurements of variations in the above-stated two types of structures to yield the final quality estimation of screen content images. Thorough experiments are conducted on three screen content image quality databases, in which the images are corrupted during capturing, compression, transmission, etc. Results demonstrate the superiority of our proposed quality model as compared with state-of-the-art relevant methods.

Evaluating Quality of Screen Content Images Via Structural Variation Analysis

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.

Generalized cumulative residual entropy and record values

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models.

Dynamic cumulative residual Renyi's entropy

https://dyuthi.cusat.ac.in/xmlui/bitstream/handle/purl/4280/Quantile%20based%20entropy%20function.pdf?sequence=1

Quantile based entropy function

In this article, we study reliability measures such as geometric vitality function and conditional Shannon's measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.

/pdf/characterizations-of-life-distributions-using-conditional-3ate2x5ok5.pdf

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

Kullback–Leibler divergence: A quantile approach

Tsallis entropy of order \(\alpha \) (see Tsallis in J Stat Phys 52(1–2):479–487, 1988) plays an important role in the measurement uncertainty of random variables. Recently, Sati and Gupta (J Probab Stat, doi:10.1155/2015/694203, 2015) introduced a cumulative Tsallis entropy of order \(\alpha \) and studied its various properties in the context of reliability modeling. In this paper, we introduce an alternate measure of cumulative Tsallis entropy of order \(\alpha \) and study its properties. Unlike the cumulative Tsallis entropy due to Sati and Gupta (J Probab Stat, doi:10.1155/2015/694203, 2015), the proposed measure has some additional features and has simple relationships with other important information and reliability measures.

S. M. Sunoj

Papers

Dynamic cumulative residual Renyi's entropy

Quantile based entropy function

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

Kullback–Leibler divergence: A quantile approach

Some properties of cumulative Tsallis entropy of order $$\alpha $$