A) Articles, papers and lecture notes
1. Regression analysis
for water table, soil salinity plant growth and
crop production

This is a book chapter dealing with the
principles
of linear regression analysis (least squares
method) including confidence statements and
segmented regression using a breakpoint.
The table of contents
may be viewed here.
One may also consult a paper on
crop production and
soil salinity : evaluation of field data
from
India by segmented linear regression with
breakpoint.

2. Crop tolerance
to soil salinity, statistical analysis
of data measured in farm lands.

This is an article published in the
International Journal of Agricultural Science
in which 8 crops in three tropical countries
(Egypt, India and Pakistan) are studied.

3.
Crop tolerance to shallow water tables, statistical
analysis of data measured in farm lands.

This is an article entered in the
ResearchGate website
in which 4 crops in 4 tropical countries
(Australia, Egypt, England, and Surinam)
are studied.

4. Frequency analysis in
hydrology

This is a book chapter dealing with the frequency
analysis of hydrologic phenomena including
lognormal (lognormal), exponential, and Gumbel
distributions giving confidence belts and
discussing return periods (recurrence
intervals).
The table of contents
may be viewed here.

5. Generalized and
composite probability distributions

This is an article published in the
International Journal of Mathematical and
Computational Methods in which the
CumFreq
and CumFreqA models are used.

6. The versatilty of the generalized
logistic probability distribution
demonstrated with examples

This is an article entered in the
ResearchGate website in which the usefulness
of this distribution that can be symmetrical,
skew to the left, or skew to the right
depending on the exponent to which the data
values are raised.

B) Free software and models
The software is totally free.
CumFreq
is meant for segmented cumulative frequency
analysis using a breakpoint (breakpoint), which
serves for example to study discontinuous
probability distributions and return periods of
hydrologic factors like rainfall, river and drain
discharge, water and river level, depth or level
of
watertable, soil salinity, hydraulic conductivity
(soil permeability for water).
The computer program fits various linear,
logarithmic, exponential and double exponential
cumulative frequency distributions, including the
normal, lognormal (lognormal), (log)logistic,
Pareto, Weibull, Frechet (FisherTippett type II),
exponential (Poissonlike) and Gumbel probability
distributions, and selects the best fitting
distribution using the method of best fit.

CumFreq for cumulative frequency analysis
and probability distribution fitting

NormDis
A twoway calculator for the standard normal
probability distribution: Value => Probability,
and
Probability => Value, which can be used for many
kinds of statistical probability analysis.

Segmented regression of mustard yield on soil
salinity

SegReg
SegReg can be used for segmented linear
regression,
i.e. regression in segments, using a breakpoint
(breakpoint) or threshold value, which serves for
example to analyse the relation between plant
growth or crop production in agriculture versus
soil salinity and depth of watertable in
agricultural land.
The segmentation is done by introducing a
breakpoint (breakpoint, threshold). Thus one can
obtain a broken, discontinuous, line.
Seven types of functions (0 to 6) are used.
Examples are given.
The selection of the best function type and
breakpoint is based on maximizing the statistical
coefficient of explanation (determination) and
performing the test of significance.
The 90% confidence interval (belt) is given
as well
as an Anova table for variance analysis.

Ftest calculator.
A calculator for the Fischer's Ftest as used in
analysis of variance (Anova). The above SegReg
model uses this test for the significannce of the
regression. Like NormDis, this is also a twoway
calculator: F => Probability, and Probability => F

ttest calculator.
A calculator for the Student's ttest as used in
the
comparison of averages (means) of data series and
determining the statistical significance of the
difference between them using the tprobability
distribution.
Like NormDis and Ftester, the ttester is also a
twoway calculator: tvalue => Probability, and
Probability => tvalue

C) Frequently asked questions
1  What are the principles of cumulative
frequency
analysis and (discontinuous) probability
distributions (used in the CumFreq program, see
Software page or below), and what to do if there
is
a discontinuity? What is return period and how
reliable is it?

This is the lecture note on
frequency
analysis.
The table of contents
can be inspected here.
An article on the use of the binomial distribution
for the determination of confidence intervals and
belts for cumulative probability distributions can
be downloaded from this
place,
while a summary of it can be found
over here

2  What are the principles of linear regression
analysis (used in the SegReg program, see Software
page or below) and how are confidence statements
and intervals determined. What is breakpoint
(break point), threshold, and coefficient of
explanation (determination)?
3  The SegReg model (see Software page) provides
confidence intervals of the breakpoint in
segmented linear regression analysis to test its
statistical significance. Is it necessary to
additionally perform an analysis of variance
(ANOVA) and Ftest and how is this done?
4  Is there a calculator available for the
Ftest
described under the previous question?
5  Is there also a calculator available for the
cumulative frequency in the standard normal
distribution?

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