A new two-parameter Lindley half-Cauchy distribution using Lindley family of distribution is introduced. The mathematical and statistical properties of the new distribution such as probability density function, cumulative distribution function, quantiles, the measure of skewness and kurtosis are presented. The parameter of the new distribution is estimated using three widely used estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. By using the maximum likelihood estimate, we have constructed the asymptotic confidence interval for the model parameters. A real data set is taken and we have compared LHC distribution with some selected distributions namely weighted Lindley, Chen, Gompertz, and Lindley. It is proven empirically that the proposed distribution is more flexible and performs better than underling distributions.
