MULTIVARIATE AREA-BIASED LINDLEY DISTRIBUTION: PROPERTIES AND APPLICATIONS
In this research paper, we have proposed multivariate area biased Lindley distribution and developed some of its statistical properties like mean, covariance, correlation and joint moments. Before proposing multivariate area biased Lindley distribution, we have first introduced area-biased Lindley distribution and have derived its various statistical properties such as mean, mode, moments, harmonic mean, and coefficient of variation, skewness and kurtosis. Expressions for Lorenz curve and entropy as a measure for uncertainty reduction are derived. The method of moments and maximum likelihood estimates of the parameter of area-biased Lindley distribution are investigated. Some reliability measures such as hazard function, mean residual life, survival function and reverse hazard rate have been studied. Area biased Lindley distribution is compared with one parameter Lindley distribution and size biased Lindley distribution by taking a real life data. We have then proposed that area biased Lindley distribution is expected to serve as a best model as compared to other models available in the statistical literature for modeling positive real data. Finally, we have extended our suggested distribution to multivariate area biased Lindley distribution and developed their expressions for mean, joint moments, covariance and correlation.