Versatile Extension of the Unit Gompertz: Efficient Estimation and Application

Amal Hassan; Asma Khalil; Heba Nagy

Makale detayları

Versatile Extension of the Unit Gompertz: Efficient Estimation and Application

Yazarlar:

Amal Hassan | Asma Khalil | Heba Nagy

Yayıncı:

Gazi University

Ana Başlıklar:

Computational Statistics | Statistical Analysis

Dergi:

Gazi University Journal of Science Vol.38 Issue 3, pp.1540-1564

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356579

pISSN:

2147-1762

Anahtar kelimeler:

Özet:

 Despite the availability of numerous statistical models for describing real-world data, the need remains for flexible distributions capable of accurately capturing diverse spread patterns, particularly within the unit interval. This study introduces the Kavya-Manoharan KM-unit Gompertz KM-UGo distribution, a novel model tailored for data confined to the unit interval. By combining the unit Gompertz distribution and the KM transformation, the KM-UGo distribution is an improved version of the existing unit-Gompertz distribution, offering more adaptability and the possibility of better model fit in a a wider range of data with diverse spread patterns. This enhances its ability to model various hazard rate shapes, including J-shaped, bathtub, increasing, inverted bathtub, and decreasing. The paper delves into the mathematical properties of the KM-UGo distribution, deriving key characteristics such as moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, and entropy measures. Classical estimation techniques, including maximum likelihood, least squares, maximum product spacing, Cramér-von Mises, Anderson-Darling, and weighted least squares are employed to determine the distributions parameters and the results are assessed using a Monte Carlo method. The studys findings showed that the maximum likelihood and maximum product spacing estimation methods offer more accurate and reliable parameter estimates. Furthermore, as demonstrated in simulation studies, larger sample sizes produce better parameter estimates, which are characterized by lower bias and higher accuracy. To illustrate its practical application, the KM-UGo distribution is applied to two real-world datasets residing within the unit interval.

 Despite the availability of numerous statistical models for describing real-world data, the need remains for flexible distributions capable of accurately capturing diverse spread patterns, particularly within the unit interval. This study introduces the Kavya-Manoharan KM-unit Gompertz KM-UGo distribution, a novel model tailored for data confined to the unit interval. By combining the unit Gompertz distribution and the KM transformation, the KM-UGo distribution is an improved version of the existing unit-Gompertz distribution, offering more adaptability and the possibility of better model fit in a a wider range of data with diverse spread patterns. This enhances its ability to model various hazard rate shapes, including J-shaped, bathtub, increasing, inverted bathtub, and decreasing. The paper delves into the mathematical properties of the KM-UGo distribution, deriving key characteristics such as moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, and entropy measures. Classical estimation techniques, including maximum likelihood, least squares, maximum product spacing, Cramér-von Mises, Anderson-Darling, and weighted least squares are employed to determine the distributions parameters and the results are assessed using a Monte Carlo method. The studys findings showed that the maximum likelihood and maximum product spacing estimation methods offer more accurate and reliable parameter estimates. Furthermore, as demonstrated in simulation studies, larger sample sizes produce better parameter estimates, which are characterized by lower bias and higher accuracy. To illustrate its practical application, the KM-UGo distribution is applied to two real-world datasets residing within the unit interval.

 Despite the availability of numerous statistical models for describing real-world data, the need remains for flexible distributions capable of accurately capturing diverse spread patterns, particularly within the unit interval. This study introduces the Kavya-Manoharan KM-unit Gompertz KM-UGo distribution, a novel model tailored for data confined to the unit interval. By combining the unit Gompertz distribution and the KM transformation, the KM-UGo distribution is an improved version of the existing unit-Gompertz distribution, offering more adaptability and the possibility of better model fit in a a wider range of data with diverse spread patterns. This enhances its ability to model various hazard rate shapes, including J-shaped, bathtub, increasing, inverted bathtub, and decreasing. The paper delves into the mathematical properties of the KM-UGo distribution, deriving key characteristics such as moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, and entropy measures. Classical estimation techniques, including maximum likelihood, least squares, maximum product spacing, Cramér-von Mises, Anderson-Darling, and weighted least squares are employed to determine the distributions parameters and the results are assessed using a Monte Carlo method. The studys findings showed that the maximum likelihood and maximum product spacing estimation methods offer more accurate and reliable parameter estimates. Furthermore, as demonstrated in simulation studies, larger sample sizes produce better parameter estimates, which are characterized by lower bias and higher accuracy. To illustrate its practical application, the KM-UGo distribution is applied to two real-world datasets residing within the unit interval.

 Despite the availability of numerous statistical models for describing real-world data, the need remains for flexible distributions capable of accurately capturing diverse spread patterns, particularly within the unit interval. This study introduces the Kavya-Manoharan KM-unit Gompertz KM-UGo distribution, a novel model tailored for data confined to the unit interval. By combining the unit Gompertz distribution and the KM transformation, the KM-UGo distribution is an improved version of the existing unit-Gompertz distribution, offering more adaptability and the possibility of better model fit in a a wider range of data with diverse spread patterns. This enhances its ability to model various hazard rate shapes, including J-shaped, bathtub, increasing, inverted bathtub, and decreasing. The paper delves into the mathematical properties of the KM-UGo distribution, deriving key characteristics such as moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, and entropy measures. Classical estimation techniques, including maximum likelihood, least squares, maximum product spacing, Cramér-von Mises, Anderson-Darling, and weighted least squares are employed to determine the distributions parameters and the results are assessed using a Monte Carlo method. The studys findings showed that the maximum likelihood and maximum product spacing estimation methods offer more accurate and reliable parameter estimates. Furthermore, as demonstrated in simulation studies, larger sample sizes produce better parameter estimates, which are characterized by lower bias and higher accuracy. To illustrate its practical application, the KM-UGo distribution is applied to two real-world datasets residing within the unit interval.

Makale detayları

Versatile Extension of the Unit Gompertz: Efficient Estimation and Application

Yazarlar:

Amal Hassan | Asma Khalil | Heba Nagy

Yayıncı:

Gazi University

Ana Başlıklar:

Computational Statistics | Statistical Analysis

Dergi:

Gazi University Journal of Science Vol.38 Issue 3, pp.1540-1564

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356579

pISSN:

2147-1762

Kavya and Manoharan

Unit Gompertz

Entropy measures

Parameter estimation

Goodness of fit tests

Sayı

Makale detayları

Versatile Extension of the Unit Gompertz: Efficient Estimation and Application

Yazarlar: Amal Hassan | Asma Khalil | Heba Nagy

Yayıncı: Gazi University

Ana Başlıklar: Computational Statistics | Statistical Analysis

Dergi: Gazi University Journal of Science Vol.38 Issue 3, pp.1540-1564

Belge Tipi: Makale

Yayın Tarihi: 1/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001356579

pISSN: 2147-1762

Kavya and Manoharan

Unit Gompertz

Entropy measures

Parameter estimation

Goodness of fit tests

Sayı

Yazarlar:

Amal Hassan | Asma Khalil | Heba Nagy

Yayıncı:

Gazi University

Ana Başlıklar:

Computational Statistics | Statistical Analysis

Dergi:

Gazi University Journal of Science Vol.38 Issue 3, pp.1540-1564

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001356579

pISSN:

2147-1762