A generalized probability distribution is developed which served as a general formula for some well known probability distributions such as weibull, exponential, rayleigh. gamma, log-nonnal. pareto. maxwell, generalized laplace etc. Besides aforesaid probahility distributions, a family of new disuibutions can also be derived from it. The statistical properties viz. moments and moment generating...

We generalize the Gaussian Mixture Autoregressive (GMAR) model to Fisher’s z (ZMAR) for modeling nonlinear time series. The consists of a mixture K-component autoregressive models with mixing proportions changing over time. This can capture series both heteroskedasticity and multimodal conditional distribution, using distribution as an innovation in MAR model. ZMAR is classified nonlinearity le...

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consid...

In this report, we propose a robust mixture of regression based on t-distribution by extending the mixture of t-distributions proposed by Peel and McLachlan (2000) to the regression setting. This new mixture of regression model is robust to outliers in y direction but not robust to the outliers with high leverage points. In order to combat this, we also propose a modified version of the propose...

Monte Carlo localization (MCL) is a Bayesian algorithm for mobile robot localization based on particle filters, which has enjoyed great practical success. This paper points out a limitation of MCL which is counter-intuitive, namely that better sensors can yield worse results. An analysis of this problem leads to the formulation of a new proposal distribution for the Monte Carlo sampling step. E...

The internal estimates of Loss Given Default (LGD) must reflect economic downturn conditions, thus estimating the “downturn LGD”, as the new Basel Capital Accord Basel II establishes. We suggest a methodology to estimate the downturn LGD distribution to overcome the arbitrariness of the methods suggested by Basel II. We assume that LGD is a mixture of an expansion and recession distribution. In...