Weibull Distribution
The Weibull distribution is flexible and commonly used in survival analysis. Its hazard function can be increasing, decreasing, or constant.
- Shape Parameter (k): Determines the shape of the hazard function.
- Scale Parameter (λ): Affects the scale of survival times.
- Applications: Suitable for modeling aging-related processes.
Gamma Distribution
The Gamma distribution is useful for modeling survival times with a variable hazard function.
- Shape Parameter (α): Governs the distribution's shape.
- Scale Parameter (β): Controls the spread of the survival times.
- Applications: Applied when survival data exhibit skewness.
Exponential Distribution
The Exponential distribution is the simplest survival model with a constant hazard rate.
- Rate Parameter (λ): Governs the constant hazard rate.
- Applications: Suitable for modeling processes with memoryless properties.
Gompertz Distribution
The Gompertz distribution is often used to model aging processes, with an exponentially increasing hazard function.
- Shape Parameter (η): Determines the rate of hazard increase.
- Scale Parameter (β): Affects the survival times.
- Applications: Common in mortality studies.
Log-Logistic Distribution
The Log-Logistic distribution is used for survival data with a non-monotonic hazard function.
- Shape Parameter (α): Governs the hazard function's shape.
- Scale Parameter (β): Affects the time scale.
- Applications: Suitable for data with long tails or recovery processes.
Log-Normal Distribution
The Log-Normal distribution models survival times that are log-normally distributed.
- Mean (μ): Mean of the logarithmic survival times.
- Standard Deviation (σ): Dispersion of the log-transformed data.
- Applications: Used when survival times exhibit log-normal characteristics.
Generalized Gamma Distribution
The Generalized Gamma distribution encompasses a wide range of distribution shapes.
- Shape Parameters (α, γ): Control the distribution's shape.
- Scale Parameter (β): Affects the scale of survival times.
- Applications: A flexible model that can approximate other distributions.
