Order Statistics Based Measure of Past Entropy

In this paper, we have proposed a measure of past entropy based on order statistics. We have studied this measure for some specific lifetime distributions. A Characterizationresult for the proposed measure has also been discussed and also and an upper bound for this measure has been derived

Theoretical Properties of the Weighted Feller-Pareto Distributions

In this paper, for the first time, a new six-parameter class of distributions called weighted Feller-Pareto (WFP) and related family of distributions is proposed. This new class of distributions contains several other Pareto-type distributions such as length-biased (LB) Pareto, weighted Pareto (WP I, II, III, and IV), and Pareto (P I, II, III, and IV) distributions as special cases. The pdf, cdf, hazard and reverse hazard functions, monotonicity properties, moments, entropy measures including Renyi, Shannon and s-entropies are derived

A NEW GENERALIZED VARENTROPY AND ITS PROPERTIES

The variance of Shannon information related to the random variable $X$, which is called varentropy, is a measurement that indicates, how the information content of $X$ is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them

Order Statistics Properties of the Two Parameter Lomax Distribution

<p>In this paper we study the distribution of order statistics of the two parametric Lomax distribution. We consider the single and product moment of order statistics from Lomax distribution.  Also, we establish some recurrence relation for single moments of order statistics. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Lomax distribution is derived.</p

An Exploratory Investigation Into the Use of eAUP as an Alternative to Text-based Passwords

Security is one of the major concerns of every industry in the world today. One of the best ways of hacking into a computer system is brute forcing. And with the increase in computing, brute forcing has become faster and easy to do. Text-based passwords are still the most popular and most commonly used form of authentication even though the requirements for a good password are still increasing. Research has shown that the best text-based passwords are the random ones that have no sequence or pattern to them. But this also makes it difficult to remember. Well- documented research has shown that it is easier to remember an image than words, hence the adage A picture is worth a thousand words. Even though there are good policies for text-based passwords, the unpredictability of users\u27 attitudes and behavior has most of the time rendered these policies inefficient. The common trade-off for the complexity of text-based passwords is recallability. Most users would prefer to use a password they can easily remember than a complex one that they can easily forget. One of the proposed alternatives to text-based passwords is graphical passwords. There are several schemes that have been proposed but are still unpopular. This thesis investigated one of these schemes that are used on mobile devices to determine whether it can be used as an alternative to text-based passwords. Also this research proposes ways to improve this scheme and options of bringing it at par with the current minimum requirements of a good text-based password

A New Generalized Varentropy and its Properties

The variance of Shannon information related to the random variable X, which is called varentropy, is a measurement that indicates, how the information content of X is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions that improved the quality of the paper

Uncertainty quantification based on residual Tsallis entropy of order statistics

In this study, we focused on investigating the properties of residual Tsallis entropy for order statistics. The reliability of engineering systems is highly influenced by order statistics, for example, when modeling the lifetime of a series system and the lifetime of a parallel system. The residual Tsallis entropy of the ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of the ith order statistics from a uniform distribution were investigated. In the mathematical framework, a method was provided to represent the residual Tsallis entropy of the ith order statistic in the continuous case with respect to the case where the distribution was uniform. This approach can provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. We also investigated the monotonicity of the new uncertainty measure under different conditions. An investigation of these properties leads to a deeper understanding of the relationship between the position of the order statistics and the resulting Tsallis entropy. Finally, we presented the computational results and proposed estimators for estimating the residual Tsallis entropy of an exponential distribution. For this purpose, we derived a maximum likelihood estimator

Quantile-Based Generalized Entropy of Order (α, β) for Order Statistics

In the present paper, we propose a quantile version of generalized entropy measure for order statistics for residual and past lifetimes and study their properties. Lower and upper bound of the proposed measures are derived. It is shown that the quantile-based generalized information between i-th order statistics and parent random variable is distribution free. The uniform, exponential, generalized Pareto and finite range distributions, which are commonly used in the reliability modeling have been characterized in terms of the proposed entropy measure with extreme order statistics