New Lindley Half Cauchy Distribution: Theory and Applications
Arun Kumar Chaudhary1, Vijay Kumar2

1Arun Kumar Chaudhary, Associate Professor, Department of Management Science, Nepal Commerce Campus, Tribhuwan University, Nepal.
2Vijay Kumar, Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, India. 

Manuscript received on October 06, 2020. | Revised Manuscript received on October 25, 2020. | Manuscript published on November 30, 2020. | PP: 1-7 | Volume-9 Issue-4, November 2020. | Retrieval Number: 100.1/ijrte.D4734119420 | DOI: 10.35940/ijrte.D4734.119420
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Abstract: In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set. 
Keywords: Estimation, Generalized Rayleigh (GR) distribution, Half-Cauchy distribution, Lindley distribution.