ABSTRACT

Modelling is challenging topic and using parametric models is important stage to reach flexible function for modelling. Weibull distribution has shape and scale parameters which play the main role for modelling. Bimodality parameter is added and so bimodal Weibull distribution can capture real data set with bimodality which can be actually combination of two populations. The properties of the proposed distribution and estimation method are examined extensively to show its usability in modelling accurately and safely for practitioners. After examination as first stage in modelling issue, it is appropriate to use bimodal Weibull for modelling bimodality in real data sets if it exists. Two estimation methods including objective functions are used to estimate the parameters of shape, scale and bimodality parameters of function. The second stage in modelling is overcome by using heuristic algorithms for optimization of function according to parameters due to the fact that converging to global point of objective function is performed by heuristic algorithms from stochastic optimization. Real data sets are provided to show the modelling competence of objective functions from bimodal forms of Weibull and Gamma distributions having well defined shape, scale and bimodality parameters and potentially less parameters when compared with the existing distributions.

摘要

建模是具有挑战性的主题，使用参数模型是实现灵活建模功能的重要阶段。Weibull 分布具有对建模起主要作用的形状和尺度参数。添加了双峰参数，因此双峰 Weibull 分布可以捕获具有双峰的真实数据集，该双峰实际上可以是两个总体的组合。对所提出的分布和估计方法的属性进行了广泛检查，以显示其在为从业者准确和安全地建模方面的可用性。在作为建模问题的第一阶段进行检查之后，如果存在真实数据集中的双峰，则适合使用双峰 Weibull 对双峰进行建模。包括目标函数在内的两种估计方法用于估计函数的形状参数、尺度参数和双峰参数。建模的第二阶段通过使用启发式算法根据参数优化函数来克服，因为收敛到目标函数的全局点是通过随机优化的启发式算法执行的。提供真实数据集以显示来自 Weibull 和 Gamma 分布的双峰形式的目标函数的建模能力，这些分布具有明确定义的形状、尺度和双峰参数，并且与现有分布相比可能具有更少的参数。