Abstract
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.
Highlights
Rao et al [1] suggested a nonnegative measure of uncertainty and called it the cumulative residual entropy (CRE)
As a natural extension of the results obtained by Noughabi [14], we study the fractional cumulative residual entropy (FCRE) and weighted cumulative residual entropy (WCRE)
For the cumulative distribution function (CDF) with support [0, 1], we exhibited that the values of CREq and CREw are within [0, e− q] and [0, 1/2e], respectively
Summary
Rao et al [1] suggested a nonnegative measure of uncertainty and called it the cumulative residual entropy (CRE). Via a comparison with other tests of uniformity, Dudewicz and Van der Meulen [9] showed that the entropy-based test possesses good power properties for many alternatives. Constructed a test for uniformity based on the CRE and studied some of its properties He reported the percentage points and power comparison against seven alternative distributions. As a natural extension of the results obtained by Noughabi [14], we study the FCRE and WCRE for testing the uniformity. Stand for convergence in n n n probability, convergence in distribution, and almost surely, as n ⟶ ∞
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