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A new trigonometric distribution with bounded support and an application. (English) Zbl 1493.62066

Summary: In this paper, we introduce a new bounded distribution by using trigonometric functions, named the cosine-sine distribution. A comprehensive study of its statistical properties is presented along with an application to a unit-interval data set, namely firms risk management cost-effectiveness data. The proposed distribution has increasing, bathtub and v hazard rate shapes. Further, we show that the distribution can be viewed as a truncated exponential sine distribution.

MSC:

62E20 Asymptotic distribution theory in statistics
62E15 Exact distribution theory in statistics
62F10 Point estimation
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[1] M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, 55. Tenth printing, 1972. · Zbl 0543.33001
[2] R. Q. Al-Faris and S. Khan, Sine square distribution: a new statistical model based on the sine function,J. Appl. Probab. Stat.3(2008), no. 1, 163-173. MR 2530366. · Zbl 1302.62042
[3] S. Chowdhury and A. K. Nanda, A new lifetime distribution with applications in inventory and insurance,Int. J. Qual. Reliab. Manag.35(2018), 527-544.
[4] D. O. Cook, R. Kieschnick and B. D. Mccullough, Regression analysis of proportions in finance with self selection,J. Empirical Finance15(2008), 860-867.
[5] A. Gen¸c, Estimation ofP(X > Y) with Topp-Leone distribution,J. Stat. Comput. Simul. 83(2013), no. 2, 326-339. MR 3015226. · Zbl 1348.62039
[6] E. G´omez-D´eniz, M. A. Sordo and E. Calder´ın-Ojeda, The Log-Lindley distribution as an alternative to the beta regression model with applications in insurance,Insurance Math. Econom.54(2014), 49-57. MR 3145850. · Zbl 1294.60016
[7] I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products, sixth edition, translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, Academic Press, San Diego, CA, 2000. MR 1773820. · Zbl 0981.65001
[8] N. A. J. Hastings and J. B. Peacock,Statistical Distributions, Halsted Press, New York, 1975. MR 0359137. · Zbl 0834.62001
[9] R. A. Jiang, A new bathtub curve model with finite supportReliab. Eng. System Safety119 (2013), 44-51.
[10] J. T. Kent and D. E. Tyler, Maximum likelihood estimation for the wrapped Cauchy distribution.J. Appl. Statist.15(1988) no. 2, 247-254.
[11] P. Kumaraswamy, Generalized probability density function for double-bounded random processes,J. Hydrology46(1980), no. 1-2, 79-88.
[12] C. D. Lai and G. Jones, Beta hazard rate distribution and applications,IEEE Trans. Reliab. 64(2015), no. 1, 44-50.
[13] C. D. Lai and S. P. Mukherjee, A note on “A finite range distribution of failure times”, Microelectron. Reliab.26(1986), no. 1, 183-189.
[14] A. W. Marshall and I. Olkin,Life Distributions, Springer Series in Statistics, Springer, New York, 2007. MR 2344835. · Zbl 1304.62019
[15] S. P. Mukherjee and A. Islam, A finite-range distribution of failure times,Naval Res. Logist. Quart.30(1983), no. 3, 487-491. MR 0717739. · Zbl 0525.62088
[16] L. E. Papke and J. M. Wooldridge, Econometric methods for fractional response variables with an application to 401(K) plan participation rates,J. Appl. Econometrics11(1996), no. 6, 619-632.
[17] A. R´enyi, On measures of entropy and information, inProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, 547-561, Univ. California Press, Berkeley, CA, 1961. MR 0132570. · Zbl 0106.33001
[18] C. E. Shannon, Prediction and entropy of printed English,Bell Syst. Tech. J.30(1951), no. 1, 50-64. · Zbl 1165.94313
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