Fit Modified Weibull-Type Distributions

Description

Fits eight modified Weibull-type distributions using maximum likelihood estimation. Returns estimates, log-likelihood, AIC, and BIC.

Usage

WeibullModiAMR(x, dist = "Alwasel2009")

Arguments

Value

A list containing:

Distributions

The following modified Weibull-type distributions are included in the package, along with their respective probability density functions (PDFs) and references:

• Rangoli2023:

  f(x) = (a b x^{b-1} + \frac{g}{x^2}) \exp(a x^b - \frac{g}{x}) \exp(-\exp(a x^b - \frac{g}{x}))

  Reference: Rangoli, A. M. (2024). doi:10.22271/maths.2024.v9.i4b.1771

• Peng2014:

  f(x) = \alpha \exp(-\lambda/x) (\beta x^{\beta-1} + \lambda x^{\beta-2}) \exp(-\alpha x^{\beta} \exp(-\lambda/x))

  Reference: Peng, X. (2014). doi:10.1016/j.ress.2013.07.007

• Lai2003:

  f(x) = a (b + l x) x^{b-1} \exp(l x) \exp(-a x^{b} \exp(l x))

  Reference: Lai, C. D. (2003). doi:10.1109/TR.2002.805788

• Xie1996:

  f(x) = (a b x^{b-1} + g l x^{l-1}) \exp(-(a x^{b} + g x^{l}))

  Reference: Xie, M. (1996). doi:10.1016/0951-8320(95)00149-2

• Sarhan2009:

  f(x) = (a b x^{b-1} + g) \exp(-(a x^{b} + g x))

  Reference: Sarhan, A. M. (2009). https://www.researchgate.net/publication/228695122_Modified_Weibull_distribution

• Rangoli2025:

  f(x) = (g l x^{l-1} + a b x^{b-1} \exp(x^{b}) / b^{a}) \exp(-((a/b^{a})(\exp(x^{b}) - 1) + g x^{l}))

  Reference: Rangoli, A. M. (2025). doi:10.7759/cureus.77347

• Mustafa2012:

  f(x) = (\alpha \beta x^{\beta-1} + \lambda \exp(-\lambda x)) \exp(-(\alpha x^{\beta} + \lambda x))

  Reference: Mustafa, A. (2012). doi:10.1016/j.ress.2013.07.007

• Alwasel2009:

  f(x) = (a + b g x^{g-1}) \exp(-(a x + b x^{g}))

  Reference: Alwasel, I. (2009). https://www.researchgate.net/publication/228817485_Statistical_Inference_of_a_Competing_Risks_Model_with_Modified_Weibull_Distributions

Examples

# Load your package
library(WeibullModiAMR)

# Example: Fit Rangoli2023 distribution
x <- rexp(50, rate = 1)
res <- WeibullModiAMR(x, dist = "Rangoli2023")
print(res)