A new class of distribution function based on the symmetric densities is introduced, these transformations also produce nonnormal distributions and its pdf and cd f can be expressed in parametric form. This class of distributions depend on the two parameters, namely g and h which controls the skewness and the elongation of the tails, respectively. This class of skewed distributions is a generalization of Tukey's g − h family of distributions.In this paper, we calculate a closed form expression for the density and distribution of the Tukey's g − h family of generalized distributions, which allows us to easily compute probabilities, moments and related measures.
This paper presents a method for approximating the underlying stock’s distribution by using a Log–Skew–Normal mixture distribution. The basic properties of a mixture of Skew–Normal distributions are reviewed in this paper. We provide a formula for the European option price by assuming that the log price follows a Skew–Normal mixture distribution. We also calculate the “Greeks”, such as delta, gamma and vega. We compare the proposed model with other existing models and consider an example of calibration to real market option data.
Mixtures of symmetric distributions, in particular normal mixtures as a tool in statistical modeling, have been widely studied. In recent years, mixtures of asymmetric distributions have emerged as a top contender for analyzing statistical data. Tukey’sgfamily of generalized distributions depend on the parameters, namely,g, which controls the skewness. This paper presents the probability density function (pdf) associated with a mixture of Tukey’sgfamily of generalized distributions. The mixture of this class of skewed distributions is a generalization of Tukey’sgfamily of distributions. In this paper, we calculate a closed form expression for the density and distribution of the mixture of two Tukey’sgfamilies of generalized distributions, which allows us to easily compute probabilities, moments, and related measures. This class of distributions contains the mixture of Log-symmetric distributions as a special case.
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