Here, we have introduced a novel probability distribution called the Weibull-Generalized inverted exponential{Log-logistic} distribution (WGIELLD) adopting the Transformed-Transformer method. The density curves of the new distribution show that it can model data sets that are approximately normal, left and right skewed; while the hazard function graphs indicate that the distribution can model components with various shapes of failure rate. We have derived various statistical features of this distribution, such as the reliability function (rf), hazard function (hf), mode, quantile function (qf), median, Renyi entropy (Re), moment generating function (mgf), mean absolute deviations (MAD) from the mean and median, and order statistics. We have used maximum likelihood estimation (MLE) approach to estimate the parameters of this distribution and also run a simulation study to verify the suitability of the approach. Finally, two sets of data are employed to demonstrate the versatility of the distribution compared to the baseline distribution and other related distributions.