<p>In this paper, a truncated Sujatha distribution has been proposed. The behaviour of its probability density function and cumulative density function has been studied. Its moment-based measures such as moments about origin, moments about mean, coefficient of variation, coefficient of skewness, coefficient of kurtosis and index of dispersion are studied. The reliability properties including survival function, hazard function, reverse hazard function and mean residual life function are studied with their graphical representation. Conditional mean and conditional variance of the proposed distribution are obtained. The proposed distribution has been shown to be a member of exponential family of distributions. The sequential probability ratio test has been discussed using the proposed distribution. Parameters of the proposed distribution are estimated using five different methods of estimation namely maximum likelihood estimation, maximum product spacing estimation, least square estimation, weighted least square estimation and Cramer–Von Mises estimation. A simulation study has also been performed to know the consistency of the estimated values of the parameters for all the five methods. The confidence interval of the estimated parameter is also presented with profile plots. Two lifetime datasets are used to demonstrate the goodness of fit of the proposed distribution; one dataset from the engineering and another one from the medical. The results of the goodness of fit demonstrates that the truncated Sujatha distribution provides a better fit over the truncated exponential distribution, truncated Lindley distribution, Sujatha distribution, Lindley distribution and exponential distribution.</p>

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The Truncated Sujatha Distribution with Properties and Applications in Engineering and Medical Sciences

  • Hosenur Rahman Prodhani,
  • Rama Shanker

摘要

In this paper, a truncated Sujatha distribution has been proposed. The behaviour of its probability density function and cumulative density function has been studied. Its moment-based measures such as moments about origin, moments about mean, coefficient of variation, coefficient of skewness, coefficient of kurtosis and index of dispersion are studied. The reliability properties including survival function, hazard function, reverse hazard function and mean residual life function are studied with their graphical representation. Conditional mean and conditional variance of the proposed distribution are obtained. The proposed distribution has been shown to be a member of exponential family of distributions. The sequential probability ratio test has been discussed using the proposed distribution. Parameters of the proposed distribution are estimated using five different methods of estimation namely maximum likelihood estimation, maximum product spacing estimation, least square estimation, weighted least square estimation and Cramer–Von Mises estimation. A simulation study has also been performed to know the consistency of the estimated values of the parameters for all the five methods. The confidence interval of the estimated parameter is also presented with profile plots. Two lifetime datasets are used to demonstrate the goodness of fit of the proposed distribution; one dataset from the engineering and another one from the medical. The results of the goodness of fit demonstrates that the truncated Sujatha distribution provides a better fit over the truncated exponential distribution, truncated Lindley distribution, Sujatha distribution, Lindley distribution and exponential distribution.