Mixture Distribution Research Papers - Academia.edu (original) (raw)

We are interested in estimating the bit error rate (BER) for signal transmission in digital communication sys- tems. Since BERs tend to be extremely small, it is difficult to obtain precise estimators based on the use of crude Monte Carlo... more

We are interested in estimating the bit error rate (BER) for signal transmission in digital communication sys- tems. Since BERs tend to be extremely small, it is difficult to obtain precise estimators based on the use of crude Monte Carlo simulation techniques. In this paper, we review, expand upon, and evaluate a number of importance sampling variance reduction techniques for estimating the BER. We find that mixtures of cer- tain "tailed" distributions with a uniform distribution produce estimators that are at least competitive with those in the literature. Our comparisons are based on analytical calculations and lay the groundwork for the evaluation of more-general mixture distributions.

The development of the rainfall occurrence model is greatly important not only for data-generation purposes, but also in providing informative resources for future advancements in water-related sectors, such as water resource management... more

The development of the rainfall occurrence model is greatly important not only for data-generation purposes, but also in providing informative resources for future advancements in water-related sectors, such as water resource management and the hydrological and agricultural sectors. Various kinds of probability models had been introduced to a sequence of dry (wet) days by previous researchers in the field. Based on the probability models developed previously, the present study is aimed to propose three types of mixture distributions, namely, the mixture of two log series distributions (LSD), the mixture of the log series Poisson distribution (MLPD), and the mixture of the log series and geometric distributions (MLGD), as the alternative probability models to describe the distribution of dry (wet) spells in daily rainfall events. In order to test the performance of the proposed new models with the other nine existing probability models, 54 data sets which had been published by several authors were reanalyzed in this study. Also, the new data sets of daily observations from the six selected rainfall stations in Peninsular Malaysia for the period 1975–2004 were used. In determining the best fitting distribution to describe the observed distribution of dry (wet) spells, a Chi-square goodness-of-fit test was considered. The results revealed that the new method proposed that MLGD and MLPD showed a better fit as more than half of the data sets successfully fitted the distribution of dry and wet spells. However, the existing models, such as the truncated negative binomial and the modified LSD, were also among the successful probability models to represent the sequence of dry (wet) days in daily rainfall occurrence.

The famous data on fatigue failure times of ball bearings have been quoted incorrectly from Lieblein and Zelen's original paper. The correct data include censored values, as well as non-fatigue failures that must be handled... more

The famous data on fatigue failure times of ball bearings have been quoted incorrectly from Lieblein and Zelen's original paper. The correct data include censored values, as well as non-fatigue failures that must be handled appropriately. They could be described by a mixture of Weibull distributions, corresponding to different modes of failure.

While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that,... more

While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modeling and predicting financial risk.

In this paper, the goodness-of-fit test based on a convex combination of Akaike and Bayesian information criteria is used to explain the features of interoccurrence times of earthquakes. By analyzing the seismic catalog of Iran for... more

In this paper, the goodness-of-fit test based on a convex combination of Akaike and Bayesian information criteria is used to explain the features of interoccurrence times of earthquakes. By analyzing the seismic catalog of Iran for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes can be described by the generalized normal distribution. This indicates that the sequence of successive earthquakes is not a Poisson process. It is found that by decreasing the threshold magnitude, the interoccurrence time distribution changes from the generalized normal distribution to the gamma distribution in some seismotectonic regions. As a new insight, the probability distribution of time intervals between earthquakes is described as a mixture distribution via the expectation-maximization algorithm.

In planning offshore wind farms, short-term wind speeds play a central role in estimating various engineering parameters, such as power output, extreme wind load, and fatigue load. Lacking wind speed time series of sufficient length, the... more

In planning offshore wind farms, short-term wind speeds play a central role in estimating various engineering parameters, such as power output, extreme wind load, and fatigue load. Lacking wind speed time series of sufficient length, the probability distribution of wind speed serves as the primary substitute for data when estimating design parameters. It is common practice to model short-term wind speeds with the Weibull distribution. Using 10-min wind speed time series at 178 ocean buoy stations ranging from 1 month to 20 years in duration ...

In some rare-event settings, exponentially twisted distributions perform very badly. One solution to this problem is to use mixture distributions. However, it is difficult to select a good mixture distribution for importance sampling. We... more

In some rare-event settings, exponentially twisted distributions perform very badly. One solution to this problem is to use mixture distributions. However, it is difficult to select a good mixture distribution for importance sampling. We here introduce a simple adaptive method for choosing good mixture importance sampling distributions.

This paper describes a semiparametric Bayesian method for analyzing duration data. The proposed estimator specifies a complete functional form for duration spells, but allows flexibility by introducing an individual het- erogeneity term,... more

This paper describes a semiparametric Bayesian method for analyzing duration data. The proposed estimator specifies a complete functional form for duration spells, but allows flexibility by introducing an individual het- erogeneity term, which follows a Dirichlet mixture distribution. I show how to obtain predictive distributions for duration data that correctly account for the uncertainty present in the model. I also