A New Generalized Logarithmic–X Family of Distributions with Biomedical Data Analysis

Zubir Shah, Dost Muhammad Khan, Zardad Khan, Nosheen Faiz, Sundus Hussain, Asim Anwar, Tanveer Ahmad, Ki Il Kim

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this article, an attempt is made to propose a novel method of lifetime distributions with maximum flexibility using a popular T–X approach together with an exponential distribution, which is known as the New Generalized Logarithmic-X Family (NGLog–X for short) of distributions. Additionally, the generalized form of the Weibull distribution was derived by using the NGLog–X family, known as the New Generalized Logarithmic Weibull (NGLog–Weib) distribution. For the proposed method, some statistical properties, including the moments, moment generating function (MGF), residual and reverse residual life, identifiability, order statistics, and quantile functions, were derived. The estimation of the model parameters was derived by using the well-known method of maximum likelihood estimation (MLE). A comprehensive Monte Carlo simulation study (MCSS) was carried out to evaluate the performance of these estimators by computing the biases and mean square errors. Finally, the NGLog–Weib distribution was implemented on four real biomedical datasets and compared with some other distributions, such as the Alpha Power Transformed Weibull distribution, Marshal Olkin Weibull distribution, New Exponent Power Weibull distribution, Flexible Reduced Logarithmic Weibull distribution, and Kumaraswamy Weibull distribution. The analysis results demonstrate that the new proposed model performs as a better fit than the other competitive distributions.

Original languageEnglish
Article number3668
JournalApplied Sciences (Switzerland)
Issue number6
Publication statusPublished - Mar 2023


  • biomedical data
  • maximum likelihood estimation
  • Monte Carlo simulation study
  • new generalized logarithmic–X family
  • Weibull distribution

ASJC Scopus subject areas

  • General Materials Science
  • Instrumentation
  • General Engineering
  • Process Chemistry and Technology
  • Computer Science Applications
  • Fluid Flow and Transfer Processes


Dive into the research topics of 'A New Generalized Logarithmic–X Family of Distributions with Biomedical Data Analysis'. Together they form a unique fingerprint.

Cite this