~187~ International Journal of Statistics and Applied Mathematics 2023; 8(6): 187-189 ISSN: 2456-1452 Maths 2023; 8(6): 187-189 © 2024 Stats & Maths https://www.mathsjournal.com Received: 01-11-2023 Accepted: 05-12-2023 Dr. K Sai Swathi Associate Professor, Department of Statistics and Computer Applications, KBR Agricultural College (ANGRAU), C.S. Puram, Andhra Pradesh, India Dr. B Guravaiah Assistant Professor, Department of Mathematics and Statistics, Vignan University, Guntur, Andhra Pradesh, India Dr. M Vijaya Lakshmi Statistics, TO Director-PME Cell, Dr. YSRH University, West Godavari, Andhra Pradesh, India GVSR Anjaneyulu Professor, Department of Statistics, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India Corresponding Author: Dr. K Sai Swathi Associate Professor, Department of Statistics and Computer Applications, KBR Agricultural College (ANGRAU), C.S. Puram, Andhra Pradesh, India Estimation of location (θ) and scale (λ) of Two- Parameter Half Logistic -Rayleigh Distribution (HLRD) using least square regression methods Dr. K Sai Swathi, Dr. B Guravaiah, Dr. M Vijaya Lakshmi and GVSR Anjaneyulu Abstract In this paper, we propose the estimation of Location (θ) and Scale (λ) parameters using the Least Square Regression Method. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under complete sample based on 1000 simulations to assess the performance of the estimators. Keywords: Two parameter HLRD, least square regression method, montecarlo simulation 1. Introduction Generally in many of the situations, we face some type of situations of non monotonic failure rates to supervise the reliability analysis of the data. In order to model such data, proposed by Aarset et al (1987) [1] and Venkataraman et al (1988) [12] proposed Least squares estimators and Weighted Least squares estimators of a Beta distribution present an extension of the Weibull family that not only contains unimodel distribution with bath tub failure rates but also allows for a broader class of monotone hazard rates and is computationally convenient for censored data. They named their extended version as “Exponentiated Weibull Family”. On similar lines Gupta and Kundu (2001b) [8] proposed a new model called generalized exponential distribution. A generalized (type – II) version of logistic distribution was considered and some interesting properties of the distribution were derived by Balakrishnan and Hassain (2007) [5] . Ramakrishna (2008) [7] studied the Type I generalized half logistic distribution scale (σ) and shape (θ) parameters estimation using the least square method in two step estimation methods. Torabi and Bagheri (2010) [13] considered different parameter estimation methods in extended generalized half logistic distribution for censored as well as complete sample. Rama Mohan and Anjaneyulu (2011) [10] studied how the least square method be good for estimating the parameters in two parameter Weibull distribution from an optimally constructed grouped sample. In Section - 2, we discuss the procedure for estimating the Location ( θ) and Scale (λ) parameters of the HLRD using the least squares regression method. We therefore employ these approximations as the least squares method. In Section - 3 we present the observations and the conclusions are based on the simulation results with the numerical example. Let x1, x2,..., xn be a random sample of size n from HLRD  (,) , its Probability Density Density Function (PDF), cumulative distribution function(CDF) and Hazard Function (HF) are given by 2 2 ( ) 2 ( ) 4( ) (;, ) ; , 0 1 x x x e fx x e         − − − − − =     +   ... (1.1)