Generalized Weibull and Inverse Weibull Distributions with Applications

In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included in the GGIW distribution are the sub-models: gamma-generalized inverse Weibull, gamma-generalized Frechet, gamma-generalized inverse Rayleigh, gamma-generalized inverse exponential, inverse Weibull, inverse Rayleigh, inverse exponential, Frechet distributions. The INMW distribution contains several sub-models including inverse Weibull, inverse new modified exponential, inverse new modified Rayleigh, new modified Frechet, inverse modified Weibull, inverse Rayleigh and inverse exponential distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, s-entropy, distribution of order statistic and Fisher information are presented. Estimates of the parameters of the models via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given

Weighted Inverse Weibull Distribution: Statistical Properties and Applications

In this paper, the weighted inverse Weibull (WIW) class of distributions is proposed and studied. This class of distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Fr´echet distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, R´enyi entropy and Fisher information are presented. Estimates of the model parameters via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given

The Gamma-Generalized Inverse Weibull Distribution with Applications to Pricing and Lifetime Data

A new distribution called the gamma-generalized inverse Weibull distribution which includes inverse exponential, inverse Rayleigh, inverse Weibull, Frechet, generalized inverse Weibull, gamma-exponentiated inverse exponential, exponentiated inverse exponential, Zografos and Balakrishnan-generalized inverse Weibull, Zografos and Balakrishnan-inverse Weibull, Zografos and Balakrishnan-generalized inverse exponential, Zografos and Balakrishnan-inverse exponential, Zografos and Balakrishnan-generalized inverse Rayleigh, Zografos and Balakrishnan-inverse Rayleigh, and Zografos and Balakrishnan-Fr\u27echet distributions as special cases is proposed and studied in detail. Some structural properties of this new distribution including density expansion, moments, Renyi entropy, distribution of the order statistics, moments of the order statistics and L-moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrate its usefulness are presented

Evolution of P-wave indices during long-term follow-up as markers of atrial substrate progression in arrhythmogenic right ventricular cardiomyopathy

AIMS: Patients with arrhythmogenic right ventricular cardiomyopathy (ARVC) have increased prevalence of atrial arrhythmias indicating atrial involvement in the disease. We aimed to assess the long-term evolution of P-wave indices as electrocardiographic (ECG) markers of atrial substrate during ARVC progression. METHODS AND RESULTS: We included 100 patients with a definite ARVC diagnosis according to 2010 Task Force criteria [34% females, median age 41 (inter-quartile range 30-55) years]. All available sinus rhythm ECGs (n = 1504) were extracted from the regional electronic ECG databases and automatically processed using Glasgow algorithm. P-wave duration, P-wave area, P-wave frontal axis, and prevalence of abnormal P terminal force in lead V1 (aPTF-V1) were assessed and compared at ARVC diagnosis, 10 years before and up to 15 years after diagnosis.Prior to ARVC diagnosis, none of the P-wave indices differed significantly from the data at ARVC diagnosis. After ascertainment of ARVC diagnosis, P-wave area in lead V1 decreased from -1 to -30 µV ms at 5 years (P = 0.002). P-wave area in lead V2 decreased from 82 µV ms at ARVC diagnosis to 42 µV ms 10 years after ARVC diagnosis (P = 0.006). The prevalence of aPTF-V1 increased from 5% at ARVC diagnosis to 18% by the 15th year of follow-up (P = 0.004). P-wave duration and frontal axis did not change during disease progression. CONCLUSION: Initial ARVC progression was associated with P-wave flattening in right precordial leads and in later disease stages an increased prevalence of aPTF-V1 was seen