Physics

Statistical inference

Exponential function

Inference

Mathematics

Algorithm

Statistical physics

Statistics

Mathematical analysis

Estimator

Artificial intelligence

Power (physics)

Computer science

Flexibility (engineering)

Exponential distribution

Quantum mechanics

Generator (circuit theory)

Applied mathematics

Exponential family

Symmetry

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science