### Tests for Parameters of Two-parametric Uniform Distribution, u(θ_1,θ_2 )

#### Abstract

*In this article, we have presented tests related to the parameters of uniform distribution defined on the interval (**q*_{1}*, **q*_{2}*). **The conditional distribution of complete sufficient statistics of the parameter of interest is obtained by conditioning the distribution of complete sufficient statistics of the nuisance parameter to be held fixed. Using this conditional distribution, uniformly most powerful unbiased (UMPU) test or uniformly most powerful invariant (UMPI) asymptotic tests have been derived for testing (i) one parameter is larger than the parameter of another distribution and (ii) the equality of parameter of two uniform distributions. Also, the corresponding power functions have been given. *

#### Keywords

#### Full Text:

PDF#### References

Lehmann EL. Testing Statistical Hypotheses. New York: Springer; 2005.

Engelhard M, Bain LJ. Uniformly most powerful unbiased tests on the scale parameter of a gamma distribution with a nuisance shape parameter. Technometric. 1977; 2: 77–81.

Perang SK. A test of equality of two exponential distributions. Statistica Neealandica. 1978; 32(2): 93–102.

Hsieh HK. On testing equality of two exponential distributions. Technometrics. 1981; 23(3): 265–269.

Nagarsenker BN, Nagarsenker PB. On a test of equality of two-parameter exponential distributions. Statistics and Probability Letters. 1984; 2: 357–361.

Nagarsenker BN, Nagarsenker PB. Distributions of LRT for testing the equality of several 2-parameter exponential distributions. IEEE Transactions on Reliability. 1985; 34(1): 65–68.

Kambo NS, Awad AM. Testing of equality of location parameters of k exponential distributions. Comm. Statist. Theory Methods. 1985; 14: 567–585.

Keating JP, Glaser RE, Ketchum N. Testing of hypotheses about the shape parameter of a gamma distribution. Technometric. 1990; 32: 67–82.

Handa BR, Kambo NS. Test of equality of two exponential distributions with common known coefficient of variation. Communication in statistics: Theory and Methods. 2005; 34(11): 2147–2155.

Al-Sahel MF, Samavi HM. Inference of overlapping coefficients in two exponential populations. Journal of Modern Applied Statistical Methods. 2007; 2(2): 503–516.

Bayoud HA, Kittaneh OA. Testing of equality of two exponential distributions. Communications in Statistics: Simulation and Computation. 2016; 47(7): 2249–2256.

Patel, S.R. On uniformly most powerful tests for truncated parameters of several one-truncation parameter family of distributions. Research and Review: Journal of Statistics. 2019; 8(2): 01–09.

Patel SR. Asymptotic tests for truncation parameters of several one-truncation parameter family of distributions. Research and Review: Journal of Statistics. 2018; 7(2): 35–41.

Patel SR. Asymptotic tests for parameters of K independent modified exponential distributions. Research and Review: Journal of Statistics. 2018; 7(3): 37–40.

Patel SR. On asymptotic testing of equality of parameters of K exponential family of distributions. International Journal of Scientific Research in Mathematical and Statistical Sciences. 2018; 5(6): 177–182.

Bhatt MB, Patel SR, Nandy PB. Asymptotic tests for parameters of two one-truncation parameters family of distributions. 2019. https://doi.org/10.1080/03610918.2019.1676440.

### Refbacks

- There are currently no refbacks.