Is there any package(s) in R for skew logistic distribution ?

Do you mean rare event logistic regression? If so, you could try the Zelig package (developed by Gary King and others), which allows you to do such analyses.

Here is an article on the topic of logistic regression in rare event data:
http://gking.harvard.edu/files/gking/files/0s.pdf 
Rpackage logistf may be used to handle such situation. The method is implemented in SAS logistic procedure also.

Thinking of rare events, if what you are looking to do is regressions, you might simply need to do a generalised linear model regression that uses the "betabinomial" distribution model, instead of regular binomial... Seems it is good for situation where the number of "successes" (events, 1's) is either very small (rare) or unusually high? There must be several packages in R that can switch to this type of distribution.

Actually, I want SKEW LOGISTIC DISTRIBUTION of Wahed and Ali (2001) [15. Wahed, A.S., Ali, M. Masoom., 2001. The skew logistic distribution, J. Stat. Res., 35, 71–80.]

R package "glogis" is specifically constructed for the generalized logistic distribution (Type I, also known as skewlogistic distribution).
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