ABSTRACT A new family of slash distributions, the modified slashed-Rayleigh distribution, is proposed and studied. This family is an extension of the ordinary Rayleigh distribution, being more flexible in terms of distributional kurtosis. It arises as a quotient of two independent random variables, one being a Rayleigh distribution in the numerator and the other a power of the exponential distribution in denominator. We present properties of the proposed family. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Finally, we conduct a small-scale simulation study to evaluate the performance of the maximum likelihood estimators and apply the results to a real data set, revealing its good performance.

The modified slashed-Rayleigh distribution offers more flexible distributional kurtosis than the ordinary Rayleigh distribution, and its parameters can be estimated using moment and maximum likelihood methods.

Modified slashed-Rayleigh distribution

Key Takeaway: The modified slashed-Rayleigh distribution offers more flexible distributional kurtosis than the ordinary Rayleigh distribution, and its parameters can be estimated using moment and maximum likelihood methods.