In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual lifetime moments, conditional moments and Rényi entropy. The parameters are estimated by the maximum likelihood method and the Fisher's information matrix is determined. Several special cases of this family are studied in some detail. An application to a real data set illustrates the performance of the family of distributions.
The paper is concerned with estimation of the probability function of a discrete random variable by minimizing the Shannon quasi-norm while meeting the moment conditions for the probability function estimated. After describing this method in detail, the paper further focuses on deriving confidence intervals for probabilities and possible application of these methods to particular data sets. and Obsahuje seznam literatury
The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.
The prediction of traffic volume over time is very important to control the flow of traffic on a road network. Traffic count is usually averaged over time to predict for the larger time domain. This paper aims at finding the detail variation of a systematic survey of hourly traffic volume data over a time of four years along the North Bengal corridor of Bangladesh (at Jamuna toll collection point) and its equivalent numerical model by using a Artificial Neural Network. The Neural Network is trained with the intermittent data of 13 weeks over four years and the missing data is interpreted with quite reasonable accuracy (12.67% MAE) with this ANN model. The ANN model captured the variety of trends of the traffic data very accurately as has been depicted in the paper
Precise wind energy potential assessment is vital for wind energy generation and planning and development of new wind power plants. This work proposes and evaluates a novel two-stage method for location-specific wind energy potential assessment. It combines accurate statistical modelling of annual wind direction distribution in a given location with supervised machine learning of efficient estimators that can approximate energy efficiency coefficients from the parameters of optimized statistical wind direction models. The statistical models are optimized using differential evolution and energy efficiency is approximated by evolutionary fuzzy rules.