Testing Statistical Hypotheses

Distribution-free statistical hypotheses testing for stochastic processes

Optimization ◽

10.1080/02331937408842222 ◽

1974 ◽

Vol 5 (7) ◽

pp. 643-656

Author(s):

R. Ahmad

Keyword(s):

Stochastic Processes ◽

Hypotheses Testing ◽

Distribution Free ◽

Statistical Hypotheses ◽

Statistical Hypotheses Testing

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Testing Statistical Hypotheses.

Journal of the Royal Statistical Society Series A (Statistics in Society) ◽

10.2307/2982206 ◽

1988 ◽

Vol 151 (1) ◽

pp. 231

Author(s):

J. D. Biggins ◽

E. L. Lehmann

Keyword(s):

Statistical Hypotheses

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Parameter estimation and testing of statistical hypotheses for diffusion type processes

Statistics of Random Processes II ◽

10.1007/978-1-4757-4293-0_7 ◽

1978 ◽

pp. 196-235

Author(s):

R. S. Liptser ◽

A. N. Shiryayev

Keyword(s):

Parameter Estimation ◽

Diffusion Type ◽

Statistical Hypotheses

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Algorithms for 3D Particles Characterization Using X-Ray Microtomography in Proppant Crush Test

Journal of Imaging ◽

10.3390/jimaging4110134 ◽

2018 ◽

Vol 4 (11) ◽

pp. 134 ◽

Cited By ~ 6

Author(s):

Ilia Safonov ◽

Ivan Yakimchuk ◽

Vladimir Abashkin

Keyword(s):

Laboratory Method ◽

X Ray ◽

Geometric Moments ◽

Before And After ◽

Statistical Hypotheses ◽

Image Processing Algorithms ◽

A New Technique ◽

Individual Particles ◽

Remarkable Advantage

We present image processing algorithms for a new technique of ceramic proppant crush resistance characterization. To obtain the images of the proppant material before and after the test we used X-ray microtomography. We propose a watershed-based unsupervised algorithm for segmentation of proppant particles, as well as a set of parameters for the characterization of 3D particle size, shape, and porosity. An effective approach based on central geometric moments is described. The approach is used for calculation of particles’ form factor, compactness, equivalent ellipsoid axes lengths, and lengths of projections to these axes. Obtained grain size distribution and crush resistance fit the results of conventional test measured by sieves. However, our technique has a remarkable advantage over traditional laboratory method since it allows to trace the destruction at the level of individual particles and their fragments; it grants to analyze morphological features of fines. We also provide an example describing how the approach can be used for verification of statistical hypotheses about the correlation between particles’ parameters and their crushing under load.

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