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The study introduces a new generalised family of distributions for cancer data modelling using a generalisation of the gamma function and a Topp-Leone-G distribution called the Gamma-Odd Topp-Leone-G (GOTL-G). Cancer data is normally characterised by complex heterogeneous properties like skewness, kurtosis, and presence of extreme values which makes it difficult to model using classical distributions. We derived multiple statistical properties including the linear representation, Re«yi entropy, quantile functions, distribution of order statistics, and maximum likelihood estimates which normally guarantees a positive effect on the generalisability of cancer data. Interestingly, we observed that these derived statistical properties make it possible for the generalisation of different models which are useful in the analysis, control, insurance, and survival of cancer patients. Our results show that this new family of distributions can be applied to a variety of data sets such as bladder and breast cancer data which exhibited high level of skewness and kurtosis as well as symmetric attributes. Therefore, we can conclude that the GOTL-G family of distributions can be extremely useful in capturing distinct complex heterogeneous properties normally exhibited by cancer patients. We recommend that this new family of distributions can be useful in modelling complex real-life applications including cancer data. [ABSTRACT FROM AUTHOR]

Abstract The goal of this research is to create a new general family of Topp-Leone distributions called the Topp-Leone Cauchy Family (TLC), which is exceedingly versatile and results from a careful merging of the Topp-Leone and Cauchy distribution families. Some of the new family’s theoretical properties are investigated using specific results on stochastic functions, quantile functions and associated measures, generic moments, probability weighted moments, and Shannon entropy. A parametric statistical model is built from a specific member of the family. The maximum likelihood technique is used to estimate the model’s unknown parameters. Furthermore, to emphasize the new family’s practical potential, we applied our model to two real-world data sets and compared it to existing rival models.

The goal of this research is to create a new general family of Topp-Leone distributions called the Topp-Leone Cauchy Family (TLC), which is exceedingly versatile and results from a careful merging of the Topp-Leone and Cauchy distribution families. Some of the new family's theoretical properties are investigated using specific results on stochastic functions, quantile functions and associated measures, generic moments, probability weighted moments, and Shannon entropy. A parametric statistical model is built from a specific member of the family. The maximum likelihood technique is used to estimate the model's unknown parameters. Furthermore, to emphasize the new family's practical potential, we applied our model to two real-world data sets and compared it to existing rival models. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize and study a new family of lifetime distributions in order to gain flexibility. The new generalized distribution is named as type II exponentiated half-logistic Topp-Leone-Marshall-Olkin-G (TIIEHL-TL-MO-G) family of distributions. Several mathematical properties of the new model have been derived including, moments and generating function, distribution of the order statistics and Rényi entropy. The performance of the maximum likelihood estimates is evaluated via a simulation study. Lastly, we apply the generated family to three real data to illustrate the potentiality of this new generalized family of distributions.

This paper aims to develop a new class of distributions, namely, type II exponentiated half-logistic Topp-Leone-G power series (TIIEHL-TL-GPS) class of distributions. Some important properties including moments, quantiles, moment generating function, entropy and maximum likelihood estimates are derived. A simulation study is conducted to evaluate the consistency of the maximum likelihood estimates. We also present three real data examples to illustrate the usefulness of the new class of distributions. Results show that the proposed model performs better than nested and several non-nested models on selected data sets. [ABSTRACT FROM AUTHOR]

In this work we focus on proposing a new lifetime Weibull type model called the transmuted Topp-Leone Weibull and studying its properties. We derive some new bivariate and multivariate transmuted Topp-Leone Weibull versions using “Farlie Gumbel Morgenstern (FGM) Copula”, “modified FGM Copula”, “Clayton Copula” and “Renyi's entropy Copula”. The estimation of its unknown parameters is carried out by considering different method of estimation. The statistical performances of all methods are studied by two real data sets and a numerical Monte Carlo simulation. The Cramer-Von Mises method is the best method for modeling the carbon fibers data. The maximum likelihood method is the best method for modeling the Leukemia data, however all other methods performed well. [ABSTRACT FROM AUTHOR]