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Stationary GE-Process and its Application in Analyzing Gold Price Data

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  • Debasis Kundu

    (Indian Institute of Technology Kanpur)

Abstract

In this paper we introduce a new discrete time and continuous state space stationary process {Xn;n = 1,2,…}, such that Xn follows a two-parameter generalized exponential (GE) distribution. Joint distribution functions, characterization and some dependency properties of this new process have been investigated. The GE-process has three unknown parameters, two shape parameters and one scale parameter, and due to this reason it is more flexible than the existing exponential process. In presence of the scale parameter, if the two shape parameters are equal, then the maximum likelihood estimators of the unknown parameters can be obtained by solving one non-linear equation and if the two shape parameters are arbitrary, then the maximum likelihood estimators can be obtained by solving a two dimensional optimization problem. Two synthetic data sets, and one real gold-price data set have been analyzed to see the performance of the proposed model in practice. Finally some generalizations have been indicated.

Suggested Citation

  • Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-021-00272-z
    DOI: 10.1007/s13571-021-00272-z
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    References listed on IDEAS

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    1. 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.
    2. Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    3. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
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