Confluent gamma density in modelling tsunami interevent times
DOI:
https://doi.org/10.6092/issn.1973-2201/4601Keywords:
gamma model, confluent hypergeometric series, G-function, tsunami eventsAbstract
We consider here a probability model which associates the usual gamma form with a confluent hypergeometric series. The probability model is termed as confluent gamma density. Some distributional properties of this model are derived. A graphical representation of the model for the varying values of parameter is illustrated. The model thrusts into an interesting application which relates it with tsunami event modelling. A study on tsunami occurrence is essential since it happens frequently at different parts of the world. Here we give an overall view about tsunamis and analyze tsunami interevent times.References
J. AITCHISON, J.A.C. BROWN (1957), The lognormal distribution with special reference to its uses in economics, Cambridge University Press.
H.K. CIGIZOGLU, M. BAYAZIT (2000), A generalized seasonal model for flow duration curve, Hydrological Processes, 14, pp. 1053-1067.
R.E. COLLIN (1960), Field Theory of Guided Waves, Mc-Graw-Hill, New York.
A. CORRAL (2004), Universal local versus unified global scaling laws in the statistics of seismicity, Physica A 340, pp. 590-597.
L.B. FELSEN, N. MARCUVITZ (1973), Radiation and Scattering of Waves, vol. 1, Englewood Cliffs: Prentice-Hall, NJ.
E.L. GEIST, T. PARSONS (2008), Distribution of tsunami interevent times, Geophysical Research Letters 35, L02612. doi: 10.1029/2007GL032690.
A.K. GUPTA, S. NADARAJAH (2006), Sums and ratios for beta Stacy distribution, Applied Mathematics and Computation 173, pp. 1310-1322.
O.A.Y. JACKSON (1969), Fitting a gamma or log-normal distribution to fibrediameter measurements on wool tops, Applied Statistics 18, pp. 70-75.
Y.Y. KAGAN (2010), Statistical distributions of earthquake numbers: consequence of branching process, Geophysical Journal International 180, pp. 1313-1328.
H.A. LAUWERIER (1951), The use of confluent hypergeometric functions in mathematical physics and the solution of an eigenvalue problem, Applied Scientific Research 2, pp. 184-204.
E. LUKACS (1955), A characterization of the Gamma distribution, The Annals of Mathematical Statistics 26(2), pp. 319-324.
S. MAHDI, M. CENAC (2006), Estimating and Assessing the Parameters of the Logistic and Rayleigh Distributions from Three Methods of Estimation, (Caribbean Journal of Mathematical and Computing Sciences) 13, pp. 25-34.
A.M. MATHAI (1993), A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford.
A.M. MATHAI (2005), A pathway to matrix - variate gamma and normal densities, Linear Algebra and its Applications 396, pp. 317-328.
A.M. MATHAI, H.J. HAUBOLD (2008), Special Functions for Applied Scientists, Springer, New York.
A.M. MATHAI, P.N. RATHIE (1971), Exact distribution of Wilks’ criterion, The Annals of Mathematical Statistics 42, pp. 1010-1019.
S.S. NAIR (2012), Statistical Distributions Connected with Pathway Model and Generalized Fractional Integral Operator, Dissertation, pp. 35-54.
S.B. PROVOST (1986), The Exact Distribution of the Ratio of a Linear Combination of Chi-Square Variables over the Root of a Product of Chi-Square Variables, The Canadian Journal of Statistics 14, pp. 61-67.
A. SAICHEV, D. SORNETTE (2007), Theory of earthquake recurrence times, Journal of Geophysical Research 112. doi:10.1029/2006JB004536.
N. SEBASTIAN (2011), A generalized gamma model associated with a Bessel function, Integral Transforms and Special Functions 22(9), pp. 631-645.
N. SEBASTIAN (2012), Statistical Distributions And Time Series Models Connected To Bessel And Mittag-Leffler Functions Via Fractional Calculus, Dissertation, pp. 43-60.
M.K. SIMON, M.S. ALOUINI (2004), Digital Communication over Fading Channels, 2nd edition, Wiley, New York.
L.J. SLATER (1960), Confluent Hypergeometric Functions, Cambridge University Press.
N.M. THOMAS (2011), Distribution of products of independently distributed pathway random variables, Statistics: A Journal of Theoretical and Applied Statistics, 47(4), pp. 861-875.
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