Extension of generalized integro-exponential function and its application in study of Chen distribution.(English)Zbl 1499.33088
Summary: In [Stat. Probab. Lett. 49, No. 2, 155–161 (2000;Zbl 0954.62117)]Z. Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function \(E^p_s(z)\) extending certain Milgram’s findings. By our novel results we derive closed-form expressions for the moments, generating function, Rényi entropy and power series for the quantile function of the Chen distribution.
MSC:
| 33E20 | Other functions defined by series and integrals |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
| 60E05 | Probability distributions: general theory |
Keywords:
Rényi entropy;Grünwald-Letnikov fractional derivative;generalized integro-exponantial function;Chen distribution;momentsCitations:
Zbl 0954.62117Cite
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