# Characterization of Extended Uniform Distribution and Its Applications

Conference paper

First Online:

## Abstract

Extended uniform distributions \(G(y)=(y/\theta )^{\alpha }, \alpha>0, \theta >0, y\in (0,\theta ]\), and its discrete version have applications in modeling random variables related to growth data, discrete and continuous (Dasgupta 2017). Notion of performance rate of a variable is elaborated and its relation with hazard rate of industrial context and density function of the variable is studied. We prove characterization theorems for a general form of extended uniform distribution based on invariance of performance rate under scale transformations in a countable dense set. Applications of the distribution in quality control in industrial production, yield data of tuber crops among others are discussed.

## Keywords

Extended uniform distribution Performance rate Hazard rate Cauchy equation Tuber crop Generalized extreme value distribution## MS Subject Classification:

Primary 62E10 Secondary 62P12## References

- Burhanuddin, M. A., Ghani, M. K. A., Ahmad, A., Abas, Z. A., & Izzah, Z. (2014). Reliability analysis of the failure data in industrial repairable systems due to equipment risk factors.
*Applied Mathematical Sciences*, 8(31), 1543–1555. https://doi.org/10.12988/ams.2014.4278.CrossRefGoogle Scholar - Dasgupta R. (2014). Characterization theorems for weibull distribution with applications.
*Journal of Environmental Statistics*. (UCLA, Dept. of Stat.),*6*(4), 1–25.Google Scholar - Dasgupta, R. (2017). Model selection and validation in agricultural context: Extended uniform distribution and some characterization theorems.
*Growth Curve Models and Applications*. Chapter 9. Springer.CrossRefGoogle Scholar - Davis, D. J. (1952). An analysis of some failure data.
*Journal of the American Statistical Association*,*47*(258), 113–150.CrossRefGoogle Scholar - Kijima, M. (1998). Hazard rate and reversed hazard rate monotonicities in continuous-time Markov chains.
*Journal of Applied Probability*,*35*, 545–556.MathSciNetCrossRefGoogle Scholar

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