We propose and investigate a new generalized family of distributions called the Topp-Leone Odd Burr III-G (TL-OBIII-G) family of distributions. We present the sub-families of this new family of distributions. Properties of the new family of distributions includs sub-models, quantile function, moments, incomplete and probability weighted moments, distribution of the order statistics, and Renyi entropy are derived. The Maximum likelihood estimation technique is used to estimate the model parameters, and a Monte Carlo simulation study is employed to examine the performance of the model. Two real datasets are used to prove the importance of the TL-OBIII-G family of distributions

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