eBook - PDF

Statistics for Mining Engineering

Name: Statistics for Mining Engineering
ISBN: 9781315815039

Jacek M. Czaplicki,

288 pages
English
PDF
Available on iOS & Android

eBook - PDF

Statistics for Mining Engineering

Jacek M. Czaplicki,

About this book

Many areas of mining engineering gather and use statistical information, provided by observing the actual operation of equipment, their systems, the development of mining works, surface subsidence that accompanies underground mining, displacement of rocks surrounding surface pits and underground drives and longwalls, amongst others. In addition, th

Information

Publisher

Year

Print ISBN

eBook ISBN

Edition

Topic

Mathematics

Subtopic

Probability & Statistics

Index

Mathematics

Fundamentals 

43

If

the

following 

inequality 

holds:

p

>

α

(1.104)

then 

there 

is

no

basis 

to

reject 

the

verified 

hypothesis 

H

0

(Figure 

1.24).

1.3.5 

Probability 

distributions 

for

the

verification 

of

statistical 

tests

Coming 

to

the

end

of

the

consideration 

of

the

basic 

terms 

used 

in

mathematical 

statistics, 

let

us

briefly 

review 

the

most 

important 

probability 

distributions 

that 

are

applied 

in

the

verifica-

tion 

of

the

statistical 

hypotheses 

that 

are

frequently 

used 

in

engineering 

practice, 

not

only 

in

mining.

Many 

tests 

are

based 

on

the

normal 

distribution 

when 

the

hypotheses 

concern 

the

param-

eters 

of

random 

variables, 

especially 

in

cases 

when 

some 

parameters 

are

known 

or

when 

the

sample 

taken 

is

large. 

However, 

when 

conditions 

of

application 

of

the

normal 

distribution 

are

not

fulfilled 

then 

several 

different 

probability 

distributions 

can

be

applied. 

These 

are:

•

the

Student’s 

t

probability 

distribution

•

the

χ

2

(chi-squared) 

probability 

distribution

•

the

F

Snedecor’s 

(Fisher-Snedecor) 

probability 

distribution.

In

some 

cases 

(see 

for

instance 

in

the

chapter 

concerning 

prediction), 

the

Fisher’s 

z

distri-

bution 

is

useful.

Figure 

1.23. 

Graphical 

illustration 

of

the

critical 

region 

determined 

by

formula 

(1.102).

Figure 

1.24. 

Graphical 

illustration 

of

the

critical 

region 

determined 

by

the

pattern 

(1.103).

Front Cover
Contents
Preface and acknowledgements
About the author
List of major notations
1. Fundamentals
2. Some areas of the application of mathematical statistics in mining
3. Analysis of data
4. Synthesis of data
5. Relationships between random variables
6. Synthesis of data—regression analysis
7. Special topic: Prediction
8. Explanations of some important terms
9. Statistical tables
References
Back Cover

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