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A Stationary Proportional Hazard Class Process and its Applications

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  • Debasis Kundu

    (Indian Institute of Technology Kanpur)

Abstract

The motivation of this work came when we were trying to analyze gold price data of the Indian market and the exchange rate data between Indian Rupees and US Dollars. It is observed that in both the cases there is a significant amount of time when $$X_n = X_{n+1}$$ X n = X n + 1 , hence they cannot be ignored. In this paper we have introduced a very flexible discrete time and continuous state space stationary stochastic process $$\{X_n\}$$ { X n } , where $$X_n$$ X n has a proportional hazard class of distribution and there is a positive probability that $$X_n = X_{n+1}$$ X n = X n + 1 . We have assumed a very flexible piecewise constant hazard function of the base line distribution of the proportional hazard class. Various properties of the proposed class has been obtained. Various dependency properties have been established. Estimating the cut points of the piecewise constant hazard function is an important problem and it has been addressed here. The maximum likelihood estimators (MLEs) of the unknown parameters cannot be obtained in closed form, and we have proposed to use profile likelihood method to compute the estimators. The gold price data set and the exchange rate data set have been analyzed and the results are quite satisfactory.

Suggested Citation

  • Debasis Kundu, 2024. "A Stationary Proportional Hazard Class Process and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10112-y
    DOI: 10.1007/s11009-024-10112-y
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    References listed on IDEAS

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    1. Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    2. Arnold, Barry C. & Hallett, J. Terry, 1989. "A characterization of the pareto process among stationary stochastic processes of the form Xn = c min(Xn-1, Yn)," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 377-380, September.
    3. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    4. Melody S. Goodman & Yi Li & Ram C. Tiwari, 2011. "Detecting multiple change points in piecewise constant hazard functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2523-2532, January.
    5. Debasis Kundu, 2023. "A stationary Weibull process and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(13), pages 2681-2700, October.
    6. Murphy, Anthony, 1996. "A piecewise-constant hazard-rate model for the duration of unemployment in single-interview samples of the stock of unemployed," Economics Letters, Elsevier, vol. 51(2), pages 177-183, May.
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