In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements.

The first ever real data application of a two-component Burr mixture distribution is provided. It is fitted to three loss data sets: fire loss claims in Denmark, fire loss claims for three building categories in Belgium and fire loss data in Norway. Each of these data sets exhibits significant bimodality. The fits of the two-component Burr mixture distribution are compared to those of five other two-component mixture distributions: the two-component Weibull mixture, two-component gamma mixture, two-component Pareto mixture, two-component lognormal mixture and the two-component exponential mixture distributions. The Burr mixture distribution is shown to give the best fit for each data set. The relative performances of the fitted distributions was assessed in terms of Akaike information criterion values, Bayesian information criterion values, consistent Akaike information criterion values, corrected Akaike information criterion values, Hannan-Quinn criterion values, density plots and probability-probability plots.

Islamic finance industry has grown fast recently especially when Arab countries make huge investments with their oil money. The rapid growth has made the industry players search for a better risk management mechanism. This has led to the introduction of Islamic options based on urbun principle. Urbun defined as deposit to the sale purchase transaction has become popular as the most viable alternative to the conventional option. This research paper's objective is to model Islamic options based on the urbun principles and shows how it can be differentiated from the conventional options. Artificial neural network has been popular recently for its application in pricing options; therefore it would be used in the research to price the Islamic option with Black-Scholes as its benchmarking. The result shows that artificial neural network is capable of pricing the Islamic options; however the lack of information provided by this model may be a concern.

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