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Multivariate Process Capability Indices for Quality Characteristics Having Nonnormal Statistical Distributions
Published in Ashis Kumar Chakraborty, Moutushi Chatterjee, Handbook of Multivariate Process Capability Indices, 2021
Ashis Kumar Chakraborty, Moutushi Chatterjee
Burr distribution finds ample application in statistical quality control, reliability and survival analysis, and failure time modelling among others. The advantage of using Burr family of distribution, as the name suggests, is that, it incorporates twelve nonnormal distributions (popularly known as Type I - Type XII) which do not require difficult computations as is required by Pearsonian system of distributions. Interested readers may refer to Kotz et al. [17] for more detail discussion on Burr distribution.
How to disseminate reliable waiting time in app-based transportation services considering attractiveness and credibility
Published in Transportmetrica A: Transport Science, 2023
Ruiya Chen, Xiangdong Xu, Anthony Chen, Xiaoning Zhang
Burr distribution has been used in travel time reliability studies (Susilawati and Somenahalli 2013; Taylor 2017). The CDF of the Burr distribution is where c and k are the shape parameters and α is the scale parameter. The parameters α and c of the 761 groups are presented in Figure 8. The parameters α and c are ranged from 124.58 to 553.45 and 7.85 to 91.08, respectively. The parameter k of the 761 groups is presented in Figure 9. The parameter k is ranged from 0.09 to 255.07. The Burr distribution has a flexible shape, which behaves on its scale and shape parameters (Taylor 2017). The broad scopes of the parameters α, c and k also indicate the flexibility and applicability of the Burr distribution among diverse datasets with spatiotemporal differences of travel time variability (i.e. different links, time periods, and days, and different statistical characteristics). This will also strengthen our analysis results based on these 761 groups, considering their statistical representativeness of the travel time data.
Flexible Heavy Tail Distributions for Surface Ozone for Selected Sites in the United States of America
Published in Ozone: Science & Engineering, 2019
I. E. Okorie, A. C. Akpanta, B. O. Osu
The Burr XII distribution (Burr 1942), hereafter called the Burr distribution for brevity, is a continuous probability distribution defined for positive random variables. The Burr distribution is also known as the Singh–Maddala distribution (Singh and Maddala 1976) and it is sometimes referred to as the generalized log-logistic distribution. The Burr distribution is widely used for modeling household income. The Burr distribution has been used in hydrological studies (Ganora and Laio 2015), meteorological studies (Mert and Karakuṣ 2015 and Mothupi et al. 2016), actuarial studies (Das and Nath 2016; Campana 2004), reliability studies (Papadopoulos 1978), transportation analysis (Susilawati, Taylor, and Somenahalli 2013), air pollution studies (Thupeng, 2016), and so on.
Transmuted Burr Type X Distribution with Covariates Regression Modeling to Analyze Reliability Data
Published in American Journal of Mathematical and Management Sciences, 2020
Muhammad Shuaib Khan, Robert King, Irene Lena Hudson
The Burr family of lifetime distributions were introduced and studied by Burr (1942) as a two-parameter family with 12 different forms of cumulative distribution functions for analyzing system failure data. In statistics literature, among those 12 distribution functions, Burr Type X and Burr Type XII received the maximum attention for studying life testing problems. The Burr distribution is a very flexible model which includes many commonly used lifetime distributions, such as gamma, lognormal, log-logistic, and beta distributions. Examples of data demonstrated by the Burr distribution are household income, crop prices, risk insurance, travel time, flood levels, and failure data.