The statistical distributions are modeled in explaining
nature of various types of data sets. Although these distributions are
mostly uni-modal, it is quite common to see multiple modes in the
observed distribution of the underlying variables, which make the
precise modeling unrealistic. The observed data do not exhibit
smoothness not necessarily due to randomness, but could also be due
to non-randomness resulting in zigzag curves, oscillations, humps
etc. The present paper argues that trigonometric functions, which
have not been used in probability functions of distributions so far,
have the potential to take care of this, if incorporated in the
distribution appropriately. A simple distribution (named as, Sinoform
Distribution), involving trigonometric functions, is illustrated in the
paper with a data set. The importance of trigonometric functions is
demonstrated in the paper, which have the characteristics to make
statistical distributions exotic. It is possible to have multiple modes,
oscillations and zigzag curves in the density, which could be suitable
to explain the underlying nature of select data set.
[1] R. Ciumara, "An actuarial model based on composite Weibull-Pareto
distribution," Mathematical Reports, vol. 8 (58), no. 4, 2006.
[2] K. Cooray and M. M. A. Ananda "Modeling actuarial data with a
composite lognormal-Pareto model," Scandinavian Actuarial Journal,
vol. 5, pp. 321-334, 2005.
[3] A. Frigessi, O. Haug and A. Rue "Dynamic mixture model for
unsupervised tail estimation without threshold selection," Extremes, vol.
5, pp. 219-235, 2002.
[4] E. Kolker, B. C. Tjaden, R. Hubley, E. N. Trifonov and A. F. Siegel
"Spectral analysis of distributions: finding periodic components in
eukaryotic enzyme length data," OMICS, Journal of Integrated Biology,
vol. 6, no.1, pp. 123-130, 2002.
[5] A. McNeil "estimating the tails of loss severity distributions using
extreme value theory," ASTIN Bulletin, vol. 27, no. 1, pp. 117-137,
1997.
[6] S. Resnick "Discussion of the Danish data on large fire insurance
losses," ASTIN Bulletin, vol.27, no.1, 139-151, 1997.
[7] D. V. S. Sastry and R. K. Sinha "A revisit to Danish fire loss data,"
Conference Proceedings, 12th Global Conference of Actuaries (GCA),
Mumbai, India, 2010.
[8] D. V. S. Sastry and R. K. Sinha "Length of stay - a data analytic
approach," Journal of Quantitative Economics, The Indian Econometric
Society, vol. 8, no. 2, pp. 42-60, 2010.
[9] D. P. M. Scollnik "On composite lognormal-Pareto model,"
Scandinavian Actuarial Journal, vol. 7, no. 1, pp. 20-33, 2007.
[1] R. Ciumara, "An actuarial model based on composite Weibull-Pareto
distribution," Mathematical Reports, vol. 8 (58), no. 4, 2006.
[2] K. Cooray and M. M. A. Ananda "Modeling actuarial data with a
composite lognormal-Pareto model," Scandinavian Actuarial Journal,
vol. 5, pp. 321-334, 2005.
[3] A. Frigessi, O. Haug and A. Rue "Dynamic mixture model for
unsupervised tail estimation without threshold selection," Extremes, vol.
5, pp. 219-235, 2002.
[4] E. Kolker, B. C. Tjaden, R. Hubley, E. N. Trifonov and A. F. Siegel
"Spectral analysis of distributions: finding periodic components in
eukaryotic enzyme length data," OMICS, Journal of Integrated Biology,
vol. 6, no.1, pp. 123-130, 2002.
[5] A. McNeil "estimating the tails of loss severity distributions using
extreme value theory," ASTIN Bulletin, vol. 27, no. 1, pp. 117-137,
1997.
[6] S. Resnick "Discussion of the Danish data on large fire insurance
losses," ASTIN Bulletin, vol.27, no.1, 139-151, 1997.
[7] D. V. S. Sastry and R. K. Sinha "A revisit to Danish fire loss data,"
Conference Proceedings, 12th Global Conference of Actuaries (GCA),
Mumbai, India, 2010.
[8] D. V. S. Sastry and R. K. Sinha "Length of stay - a data analytic
approach," Journal of Quantitative Economics, The Indian Econometric
Society, vol. 8, no. 2, pp. 42-60, 2010.
[9] D. P. M. Scollnik "On composite lognormal-Pareto model,"
Scandinavian Actuarial Journal, vol. 7, no. 1, pp. 20-33, 2007.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56748", author = "R K Sinha", title = "A Thought on Exotic Statistical Distributions", abstract = "The statistical distributions are modeled in explaining
nature of various types of data sets. Although these distributions are
mostly uni-modal, it is quite common to see multiple modes in the
observed distribution of the underlying variables, which make the
precise modeling unrealistic. The observed data do not exhibit
smoothness not necessarily due to randomness, but could also be due
to non-randomness resulting in zigzag curves, oscillations, humps
etc. The present paper argues that trigonometric functions, which
have not been used in probability functions of distributions so far,
have the potential to take care of this, if incorporated in the
distribution appropriately. A simple distribution (named as, Sinoform
Distribution), involving trigonometric functions, is illustrated in the
paper with a data set. The importance of trigonometric functions is
demonstrated in the paper, which have the characteristics to make
statistical distributions exotic. It is possible to have multiple modes,
oscillations and zigzag curves in the density, which could be suitable
to explain the underlying nature of select data set.", keywords = "Exotic Statistical Distributions, Kurtosis, Mixture
Distributions, Multi-modal", volume = "6", number = "1", pages = "45-4", }