Tsallis and Kaniadakis Entropy Measures for Risk Neutral Densities

Computer Aided Systems Theory – EUROCAST 2017 - Lecture Notes in Computer Science ◽

10.1007/978-3-319-74727-9_7 ◽

2018 ◽

pp. 55-63

Author(s):

Muhammad Sheraz ◽

Vasile Preda ◽

Silvia Dedu

Keyword(s):

Entropy Measures ◽

Risk Neutral

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Entropy Measures in Finance and Risk Neutral Densities

10.3390/ecea-2-b005 ◽

2015 ◽

Author(s):

MUHAMMAD SHERAZ ◽

Vasile Preda

Keyword(s):

Entropy Measures ◽

Risk Neutral

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D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽

10.1027/1614-2241/a000026 ◽

2011 ◽

Vol 7 (3) ◽

pp. 88-95 ◽

Cited By ~ 2

Author(s):

Jose A. Martínez ◽

Manuel Ruiz Marín

Keyword(s):

Symbolic Dynamics ◽

Scale Invariance ◽

Rating Scales ◽

Rating Scale ◽

Marketing Research ◽

Response Patterns ◽

Measurement Scales ◽

Improve Measurement ◽

Entropy Measures ◽

The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

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