Testing exponentiality for imprecise data and its application
The goodness-of-fit test for a given data set is an important problem in statistical inference and its applications. In this paper, we consider this problem for the exponential distribution which is widely used in the various areas under fuzzy environment. To this end, we need an approach that the most commonly used tests in statistics such as Kolmogorov–Smirnov and Anderson–Darling are made usable for fuzzy data set. For this purpose, we use the \(\alpha \)-pessimistic technique and Monte Carlo simulation method.
KeywordsGoodness-of-fit test Exponential distribution Fuzzy data set \(\alpha \)-Pessimistic Monte Carlo simulation
The authors thank the Associate Editor and anonymous referees for making some valuable suggestions which led to a considerable improvement in the presentation of this manuscript.
Compliance with ethical standards
Conflict of interest
The authors declare no (financial or non-financial) potential conflicts of interest.
Human and animal rights
This article does not contain any studies with human participants or animals performed by any of the authors.
- Alizadeh Noughabi H, Akbari MG (2016) Testing normality based on fuzzy data. Int J Intell Technol Appl Stat 9(1):37–52Google Scholar
- Liu B (2014) Uncertainty theory. Springer, BerlinGoogle Scholar
- Peng J, Liu B (2004) Some properties of optimistic and pessimistic values of fuzzy variables. In: IEEE international conference on fuzzy systemsGoogle Scholar
- Sedra A, Smith K (2004) Microelectronic circuits. Oxford University Press, OxfordGoogle Scholar
- Wei Y, Wang M, Qiu J (2013) New approach to delay-dependent H filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions. IET Control Theory Appl 7(5):684–696Google Scholar
- Wei Y, Qiu J, Karimi HR, Wang M (2014) Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information. Inf Sci 269(10):316–331Google Scholar