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Cancer Data Modelling: Application of the Gamma-Odd Topp-Leone-G Family of Distributions
Modelado de datos sobre el cáncer: aplicación de la familia de distribuciones GammaOdd Topp-Leone-G
DOI:
https://doi.org/10.15446/rce.v47n2.112929Keywords:
exponentiated general distribution, gamma function, Maximum likelihood estimation, Topp-Leone Distribution, Cancer Modelling (en)Distribución general exponenciada, Función gamma, Estimación de máxima verosimilitud, Topp-Leone, Modelado de cáncer. (es)
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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, Renyi 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 xhibited 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.
El estudio presenta una nueva familia generalizada de distribuciones para el modelado de datos sobre cáncer utilizando una generalización de la función gamma y una distribución Topp-Leone-G llamada Gamma-Odd Topp-Leone-G (GOTL-G). Los datos sobre el cáncer normalmente se caracterizan por propiedades heterogéneas complejas como asimetría, curtosis y presencia de valores extremos, lo que dificulta el modelado utilizando distribuciones clásicas. Derivamos múltiples propiedades estadísticas, incluida la representación lineal, la entropía de Re'nyi, funciones cuantiles, estadísticas de distribución de orden y estimaciones de máxima verosimilitud, que normalmente garantizan un efecto positivo en la generalización de los datos sobre el cáncer. Curiosamente, observamos que estas propiedades estadísticas derivadas permiten la generalización de diferentes modelos que son útiles en el análisis, control, seguro y supervivencia de pacientes con cáncer. Nuestros resultados muestran que esta nueva familia de distribuciones se puede aplicar a una variedad de conjuntos de datos, como datos de cáncer de vejiga y de mama, que mostraron un alto nivel de asimetría y curtosis, así como atributos simétricos. Por lo tanto, podemos concluir que la familia de distribuciones GOTL-G puede ser extremadamente útil para capturar distintas propiedades heterogéneas complejas que normalmente exhiben los pacientes con cáncer. Recomendamos que esta nueva familia de distribuciones pueda resultar útil para modelar aplicaciones complejas de la vida real, incluidos datos sobre cáncer.
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