A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a ...

Ateya and Madhagi (2011) introduced a multivariate form of truncated generalized Cauchy distribution (TGCD), which introduced by Ateya and Al-Hussaini (2007). The multivariate version of (TGCD) is denoted by (MVTGCD). Among the features of this form are that subvectors and conditional subvectors of random vectors, distributed according to this distribution, have the same form of distribution ...

The mixture of factor analyzers model, which has been used successfully for the model-based clustering of high-dimensional data, is extended to generalized hyperbolic mixtures. The development of a mixture of generalized hyperbolic factor analyzers is outlined, drawing upon the relationship with the generalized inverse Gaussian distribution. An alternating expectation-conditional maximization a...

We show that when asset returns satisfy a location-scale property (possibly conditionally as e.g. for multivariate generalized hyperbolic distribution) and the investor has law-invariant increasing preferences, optimal investment portfolio always exhibits two-fund or three-fund separation. As consequence, we recover many of (and two-fund) separation theorems have been derived in literature unde...

The estimation of multivariate GARCH models remains a challenging task, even in modern computer environments. This manuscript shows how Independent Component Analysis can be used to estimate the Generalized Orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univ...

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to t exceptionally well to the empirical distribution of stock returns. We review the background of hyper-bolic distributions and prove stationary distributions of certain GARCH-type models to be generalized hyperbolic.

In this study, we define a generalized hyperbolic secant distribution. Poor fit to heavy tailed data sets is repeatedly obtained by existing three-parameter distributions. Only three parameters are considered in the proposed new distribution and it fits left- right-tailed better than various We study some properties of distribution, namely, mode, skewness, kurtosis, hazard function, moments, me...

A mixture of coalesced generalized hyperbolic distributions (GHDs) is developed by joining a finite mixture of generalized hyperbolic distributions with a novel mixture of multiple scaled generalized hyperbolic distributions (MSGHDs). After detailing the development of the mixture of MSGHDs, which arises via implementation of a multidimensional weight function, the density of our coalesced dist...