  The linear exponential distribution is a generalization of the exponential
and Rayleigh distributions. This distribution is one of the best models to fit
data with increasing failure rate (IFR). But it does not provide a reasonable
fit for modeling data with decreasing failure rate (DFR) and bathtub shaped
failure rate (BTFR). To overcome this drawback, we propose a new record-based
transmuted generalized linear exponential (RTGLE) distribution by using the
technique of Balakrishnan and He (2021). The family of RTGLE distributions is
more flexible to fit the data sets with IFR, DFR, and BTFR, and also
generalizes several well-known models as well as some new record-based
transmuted models. This paper aims to study the statistical properties of RTGLE
distribution, like, the shape of the probability density function and hazard
function, quantile function and its applications, moments and its generating
function, order and record statistics, Renyi entropy. The maximum likelihood
estimators, least squares and weighted least squares estimators,
Anderson-Darling estimators, Cramer-von Mises estimators of the unknown
parameters are constructed and their biases and mean squared errors are
reported via Monte Carlo simulation study. Finally, the real data set based on
failure time illustrates the goodness of fit and applicability of the proposed
distribution; hence, suitable recommendations are forwarded.
