scholarly journals Information Measure in Terms of the Hazard Function and Its Estimate

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 298
Author(s):  
Sangun Park
Keyword(s):  
Fisher Information ◽  
Hazard Function ◽  
Information Measure ◽  
Test Statistic ◽  
Information Measures ◽  
Leibler Information ◽  
Anderson Darling

It is well-known that some information measures, including Fisher information and entropy, can be represented in terms of the hazard function. In this paper, we provide the representations of more information measures, including quantal Fisher information and quantal Kullback-leibler information, in terms of the hazard function and reverse hazard function. We provide some estimators of the quantal KL information, which include the Anderson-Darling test statistic, and compare their performances.

Parametric R-norm directed-divergence convex function

2016 ◽  
Vol 19 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Dhanesh Garg ◽  
Satish Kumar
Keyword(s):  
Convex Function ◽  
Industrial Engineering ◽  
Information Measure ◽  
Divergence Measure ◽  
Directed Divergence ◽  
Information Measures ◽  
New Information ◽  
Special Cases ◽  
Leibler Information

In this paper, we define parametric [Formula: see text]-norm directed-divergence convex function and discuss their special cases and prove some properties similar to Kullback–Leibler information measure. From [Formula: see text]-norm divergence measure new information measures have also been derived and their relations with different measures of entropy have been obtained and give its application in industrial engineering.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

scholarly journals A permutation information theory tour through different interest rate maturities: the Libor case

2015 ◽  
Vol 373 (2056) ◽  
pp. 20150119 ◽  
Author(s):  
Aurelio Fernández Bariviera ◽  
María Belén Guercio ◽  
Lisana B. Martinez ◽  
Osvaldo A. Rosso
Keyword(s):  
Information Theory ◽  
Interest Rate ◽  
Interest Rates ◽  
Fisher Information ◽  
Shannon Entropy ◽  
Anomalous Behaviour ◽  
Information Measure ◽  
Special Mechanism ◽  
Fisher Information Measure ◽  
Japanese Yen

This paper analyses Libor interest rates for seven different maturities and referred to operations in British pounds, euros, Swiss francs and Japanese yen, during the period 2001–2015. The analysis is performed by means of two quantifiers derived from information theory: the permutation Shannon entropy and the permutation Fisher information measure. An anomalous behaviour in the Libor is detected in all currencies except euros during the years 2006–2012. The stochastic switch is more severe in one, two and three months maturities. Given the special mechanism of Libor setting, we conjecture that the behaviour could have been produced by the manipulation that was uncovered by financial authorities. We argue that our methodology is pertinent as a market overseeing instrument.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

scholarly journals Multidimensional Computerized Adaptive Testing Using Non-Compensatory Item Response Theory Models

2018 ◽  
Vol 43 (6) ◽  
pp. 464-480
Author(s):  
Chia-Ling Hsu ◽  
Wen-Chung Wang
Keyword(s):  
Item Response Theory ◽  
Mutual Information ◽  
Item Response ◽  
Fisher Information ◽  
Computerized Adaptive Testing ◽  
Test Reliability ◽  
Information Method ◽  
Leibler Information ◽  
Termination Criterion ◽  
Latent Traits

Current use of multidimensional computerized adaptive testing (MCAT) has been developed in conjunction with compensatory multidimensional item response theory (MIRT) models rather than with non-compensatory ones. In recognition of the usefulness of MCAT and the complications associated with non-compensatory data, this study aimed to develop MCAT algorithms using non-compensatory MIRT models and to evaluate their performance. For the purpose of the study, three item selection methods were adapted and compared, namely, the Fisher information method, the mutual information method, and the Kullback–Leibler information method. The results of a series of simulations showed that the Fisher information and mutual information methods performed similarly, and both outperformed the Kullback–Leibler information method. In addition, it was found that the more stringent the termination criterion and the higher the correlation between the latent traits, the higher the resulting measurement precision and test reliability. Test reliability was very similar across the dimensions, regardless of the correlation between the latent traits and termination criterion. On average, the difficulties of the administered items were found to be at a lower level than the examinees’ abilities, which shed light on item bank construction for non-compensatory items.

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