Axioms,
Journal Year:
2023,
Volume and Issue:
12(4), P. 350 - 350
Published: April 1, 2023
The
choice
of
an
appropriate
regression
model
for
econometric
modeling
minimizes
information
loss
and
also
leads
to
sound
inferences.
In
this
study,
we
develop
four
quantile
models
based
on
trigonometric
extensions
the
unit
generalized
half-normal
distributions
a
bounded
response
variable
defined
interval.
desirable
shapes
these
distributions,
such
as
left-skewed,
right-skewed,
reversed-J,
approximately
symmetric,
bathtub
shapes,
make
them
competitive
responses
with
traits.
maximum
likelihood
method
is
used
estimate
parameters
models,
Monte
Carlo
simulation
results
confirm
efficiency
method.
We
demonstrate
utility
our
by
investigating
relationship
between
OECD
countries’
educational
attainment
levels,
labor
market
insecurity,
homicide
rates.
diagnostics
reveal
that
all
provide
good
fit
data
because
residuals
are
well
behaved.
A
comparative
analysis
shows
best.
However,
sine
(SUGHN)
best
overall.
It
observed
insecurity
rate
have
significant
negative
effects
values
countries.
Analytics,
Journal Year:
2023,
Volume and Issue:
2(2), P. 438 - 462
Published: May 16, 2023
The
use
of
distributions
to
model
and
quantify
risk
is
essential
in
assessment
management.
In
this
study,
the
generalized
unit
half-logistic
geometric
(GUHLG)
distribution
developed
bounded
insurance
data
on
interval.
corresponding
probability
density
function
plots
indicate
that
related
can
handle
exhibit
left-skewed,
right-skewed,
symmetric,
reversed-J,
bathtub
shapes.
hazard
rate
also
suggests
be
applied
analyze
with
bathtubs,
N-shapes,
increasing
failure
rates.
Subsequently,
inferential
aspects
proposed
are
investigated.
particular,
Monte
Carlo
simulation
exercises
carried
out
examine
performance
estimation
method
by
using
an
algorithm
generate
random
observations
from
quantile
function.
results
suggest
considered
efficient.
univariate
application
multivariate
associated
regression
survey
reveal
provides
a
better
fit
than
other
existing
models.
Under
application,
we
estimate
parameters
both
maximum
likelihood
Bayesian
estimations.
estimates
for
two
methods
very
close.
Diagnostic
trace,
ergodic,
autocorrelation
chains
converge
stationary
distribution.
GAZI UNIVERSITY JOURNAL OF SCIENCE,
Journal Year:
2025,
Volume and Issue:
unknown, P. 1 - 1
Published: April 26, 2025
This
study
proposes
the
unit
Gamma-Lindley
distribution,
a
novel
bounded
statistical
model
that
extends
flexibility
of
existing
distributions
for
modeling
data
on
(0,1)
interval.
The
proposed
distribution
is
characterized,
by
closed-form
expressions
derived
its
cumulative
probability
density,
and
hazard
rate
functions.
Some
properties,
including
moments,
order
statistics,
Bonferroni,
Lorenz
curves,
entropy,
etc.
are
examined.
To
estimate
unknown
parameters,
several
estimation
methods
introduced
their
performance
assessed
through
Monte
Carlo
simulation
experiment
based
bias
mean
square
error
criteria.
A
real
application
focusing
firm
management
cost-effectiveness
highlights
practical
utility
model,
demonstrating
superior
fit
compared
to
current
distributions,
such
as
beta
Kumaraswamy.
Furthermore,
regression
developed
with
parameter
performed
using
maximum
likelihood
method.
new
provides
an
alternative
analyzing
response
variables.
findings
contribute
literature
offering
flexible
comprehensive
framework
data,
theoretical
advancements
applicability.
Mathematics,
Journal Year:
2023,
Volume and Issue:
11(2), P. 448 - 448
Published: Jan. 14, 2023
Income
modeling
is
crucial
in
determining
workers’
earnings
and
an
important
research
topic
labor
economics.
Traditional
regressions
based
on
normal
distributions
are
statistical
models
widely
applied.
However,
income
data
have
asymmetric
behavior
best
modeled
by
non-normal
distributions.
The
objective
of
this
work
to
propose
parametric
quantile
two
distributions:
Dagum
Singh–Maddala.
proposed
regression
reparameterizations
the
original
inserting
a
parameter.
We
present
reparameterizations,
properties
distributions,
with
their
inferential
aspects.
proceed
Monte
Carlo
simulation
studies,
considering
performance
evaluation
maximum
likelihood
estimation
analysis
empirical
distribution
types
residuals.
results
show
that
both
meet
expected
outcomes.
apply
household
set
provided
National
Institute
Statistics
Chile.
good
model
fitting.
Thus,
we
conclude
obtained
favor
Singh–Maddala
for
positive
asymmetrically
distributed
related
incomes.
economic
implications
our
investigation
discussed
final
section.
Hence,
proposal
can
be
valuable
addition
tool-kit
applied
statisticians
econometricians.
Fractal and Fractional,
Journal Year:
2023,
Volume and Issue:
7(2), P. 169 - 169
Published: Feb. 7, 2023
Covariate-related
response
variables
that
are
measured
on
the
unit
interval
frequently
arise
in
diverse
studies
when
index
and
proportion
data
of
interest.
A
regression
mean
is
commonly
used
to
model
this
relationship.
Instead
relying
mean,
which
sensitive
atypical
less
general,
we
can
estimate
such
a
relation
using
fractile
regression.
point
probability
density
curve
area
under
between
origin
equal
specified
fraction.
Fractile
or
quantile
modeling
has
been
considered
for
some
statistical
distributions.
Our
objective
present
article
formulate
novel
based
parametric
distribution.
developed
reparameterizing
initial
Then,
introduce
functional
form
through
link
function.
The
main
features
new
distribution,
as
well
density,
functions,
obtained.
We
consider
brand-new
distribution
fractiles
continuous
dependent
variable
(response)
bounded
(0,
1).
discuss
an
R
package
with
random
number
generators
functions
cumulative
quantile,
addition
estimation
checking.
original
distribution-free
regression,
lately
employed
several
investigations.
use
fit
apply
it
two
case
COVID-19
medical
from
Brazil
United
States
illustration.
PLoS ONE,
Journal Year:
2022,
Volume and Issue:
17(11), P. e0276695 - e0276695
Published: Nov. 3, 2022
In
many
practical
situations,
there
is
an
interest
in
modeling
bounded
random
variables
the
interval
(0,
1),
such
as
rates,
proportions,
and
indexes.
It
important
to
provide
new
continuous
models
deal
with
uncertainty
involved
by
of
this
type.
This
paper
proposes
a
quantile
regression
model
based
on
alternative
parameterization
unit
Burr
XII
(UBXII)
distribution.
For
UBXII
distribution
its
associated
regression,
we
obtain
score
functions
observed
information
matrices.
We
use
maximum
likelihood
method
estimate
parameters
model,
conduct
Monte
Carlo
study
evaluate
performance
estimates
samples
finite
size.
Furthermore,
present
general
diagnostic
analysis
selection
techniques
for
model.
empirically
show
importance
flexibility
through
application
actual
data
set,
which
dropout
proportion
Brazilian
undergraduate
animal
sciences
courses
analyzed.
statistical
learning
comparing
proposed
beta,
Kumaraswamy,
unit-Weibull
regressions.
The
results
that
provides
best
fit
most
accurate
predictions.
Therefore,
it
valuable
competitive
well-known
regressions
double-bounded
interval.
Mathematics,
Journal Year:
2022,
Volume and Issue:
10(17), P. 3035 - 3035
Published: Aug. 23, 2022
Several
papers
on
distributions
to
model
rates
and
proportions
have
been
recently
published;
their
fitting
in
numerous
instances
is
better
than
the
alternative
beta
distribution,
which
has
distribution
follow
when
it
necessary
quantify
average
of
a
response
variable
based
set
covariates.
Despite
great
usefulness
this
fit
responses
(0,1)
unit
interval,
its
relevance
loses
objectivity
interest
quantifying
influence
these
covariates
quantiles
(0,1);
being
most
critical
situation
presents
high
asymmetry
and/or
kurtosis.
The
main
objective
work
introduce
for
modeling
proportions.
introduced
obtained
from
alpha-power
extension
skew–normal
known
literature
as
power–skew–normal
distribution.
