Abstract
Janardan Distribution is one of the important distributions from lifetime models and it has many applications in real life data. A size-biased form of the two parameter Janardan distribution has been introduced in this paper, of which the size-biased Lindley distribution is a special case. Its moments, median, skewness, kurtosis and Fisher index of dispersion are derived and compared with the size-biased Lindley distribution. The shape of the size-biased Janardan distribution is also discussed with graphs. The survival function and hazard rate of the size-biased Janardan distribution have been derived and it is concluded that the hazard rate of the distribution is monotonically increasing. The flexibility in the reliability measures of the size-biased Janardan distribution have been discussed by stochastic ordering. To estimate the parameters of the size-biased Janardan distribution maximum likelihood equations are developed.
Highlights
Size-biased distributions are the special cases of the weighted distributions. [6] introduced the weighted distributions to model ascertainment bias and later was discussed by [13]. [11] & [12] discussed the applications of weighted distributions and size biased sampling in real life
As we know that the Janardan Distribution has wide applicationsin lifetime models
A size-biased form of the two parameter Janardan distribution is derived in this paper and it has been noted that it is a special case of the size-biased Lindley distribution
Summary
Size-biased distributions are the special cases of the weighted distributions. [6] introduced the weighted distributions to model ascertainment bias and later was discussed by [13]. [11] & [12] discussed the applications of weighted distributions and size biased sampling in real life. [16] introduced a two parameter continuous distribution named as Janardan distribution (JD) and derived its various properties including moments, failure rate function, mean residual life function and stochastic ordering They discussed the estimation methods for JD and apply it on waiting time data. It is observed that for α = 1 , the SBJD (5) approaches to size-biased Lindley distribution (SBLD) with probability density function f [15] introduced the mixture of Poisson and Janardan distribution named discrete Poisson-Janardan distribution (PJD) They developed properties and parameter estimation of the PJD and applied it on two data sets, distribution of mistakes in copying groups of random digits and distribution of Pyrausta nublilalis.[4] derived Poisson area-biased Lindley distribution including its structural properties.
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