REFLECTION

A comparison of Exponentiated Exponential (EE) distribution and Generalised Beta distribution of Second kind (GB2)

Haris M, Naiju M Thomas — Sun, 31 May 2026 00:00:00 +0000

This study presents a comprehensive comparison of Exponentiated
Exponential(EE) distribution and Generalised Beta distribution
of second kind(GB2) based on their properties, parameter estimation
techniques, and goodness-of-fit measures. The both Exponentiated
Exponential and Generalised Beta distribution of second kind are life
time distributions and widely used in statistical modeling due to their
flexibility in capturing various data behaviors used to fit skewed, positive
data such as income, reliability, and survival times. But they
differ in complexity and tail behavior. The important statistical characteristics
including moments, hazard functions, fitted values, and entropy
measurements were discussed. Parameters are estimated using
Bayesian estimation techniques and Maximum Likelihood Estimation
(MLE), AIC (Akaike Information Criterion), BIC (Bayesian Information
Criterion) and Shannon differential entropy.

Static Stress Strain Analysis in a Laterally Inhomogeneous Lithosphere-Asthenosphere System

Debnath S K, Dutta T, Ghosh U., Biswas S — Sun, 31 May 2026 00:00:00 +0000

Noting that the Real Earth being highly laterally inhomogeneous
where, the rigidity of the material of the Earth gradually increases/
decreases as we go apart from any earthquake fault .In the present
paper the lithosphere- asthenosphere system is considered up to a
depth of 200 km. from the free surface where rigidity is assumed
to vary linearly with distance from the fault. We have tried to de-
velop a mathematical model to investigate the e ect of this variation
of rigidity with distance on stress and strain accumulation/release
in the lithosphere-asthenosphere system due to the movement across
the long strike slip fault assumed to be situated vertically and sur-
face breaking. The associated boundary value problem is numerically
solved by nite di erence method in presence of discontinuity and
a MATLAB program is developed. It is found that the continuous
change of rigidity with distance from the fault has considerable e ect
on the nature of stress-strain accumulation /release in the system as
compared to the elastic half-space and elastic layered model.

Analyzing Ocular Diseases Through Persistence Diagrams and Topological Data Analysis

Surayya KR, Dr. Vinitha T — Sun, 31 May 2026 00:00:00 +0000

This study explores the topological characteristics of affected eyes through
the framework of Topological Data Analysis (TDA), with a focus on Betti
numbers derived from persistence diagrams. A dataset comprising retinal
images of both normal and disease affected eyes was analyzed using Ripser,
a tool for computing persistent homology in grayscale images. By extracting
Betti numbers (β0 and β1) from the persistence diagrams, we quantitatively
captured the topological features such as connected components and
loops present in each image. Comparative analysis revealed notable differences
in the distribution of Betti numbers between normal and disease eyes,
indicating measurable alterations in the topological structure of disease affected
eyes. These findings highlight the potential of TDA as a non-invasive
and quantitative method for distinguishing ocular health conditions based on
topological invariants.

Time Series Prediction of Wind Power using Autoregressive- Moving Average Model

Vinitha Varghese, Divya P. S, Amala Linus — Sun, 31 May 2026 00:00:00 +0000

Proper forecasting of wind is a significant requirement for an effective
way of incorporating renewable energy in contemporary power
systems. The nonlinear and highly changing nature of wind speed
is difficult to forecast, particularly when it comes to models of the
wind power curve, which is a union of wind speed and power output.
This paper uses the Auto Regressive Moving Average (ARMA)
model to predict the wind power curves based on the past wind speedpower
records. Being a time series model, the ARMA model is used
to represent the time variation in the data and offer predictions with
a statistical basis. The standard error measures that were used to
evaluate model performance with Mean Absolute Error (MAE) and
Root Mean Square Error (RMSE). Conclusions provided find that,
using the ARMA model can give credible predictions of wind power
curves; it is a simple, although effective method to forecast wind energy.
The results not only emphasize the Autoregressive Moving Average
Modeling as a statistical tool to integrate renewable energy, but
also establish the basis to do more research on it, which may include
some hybrid and ensemble approaches to represent an even better
forecasting pinnacle.

Modelling of Wind Speed Data Using Weibull, Champernowne & Johnson SB Distributions

Amala Linus, Vinitha Varghese, Divya P. S — Sun, 31 May 2026 00:00:00 +0000

The wind speed data must be modelled correctly using the appropriate
probability distributions so that we can assess the wind energy potential in
an effective way. In this paper, wind speed data from three different sites
are modelled using Weibull, Champernowne & Johnson SB distributions.
Their parameters are estimated using Maximum Likelihood Estimation
(MLE) and Least Square Method. The fit is validated using the Goodness
of Fit tests - Kolmogorov-Smirnov (KS) test, Akaike Information Criterion
(AIC) and Bayesian Information Criterion (BIC). The analysis shows that
for the first site, Johnson SB gives the best fit with lower BIC. For second
and third sites, Champernowne distribution gives the best fit. The performance
of Weibull distribution was not good, as it scored high AIC and BIC
values across all sites. From the study, we are able to suggest Johnson SB
and Champernowne distributions as an alternative to conventional Weibull
distribution. It is essential to consider the local wind characteristics while
selecting distributions for wind energy modelling

Distribution of Concomitants from the Generalized Morgenstern Type Bivariate Exponential Distribution

Biju Thomas, Preethi John — Sun, 31 May 2026 00:00:00 +0000

The generalized bivariate Morgenstern family extends the classical Morgenstern
framework to enhance the dependence structure between variables.
This study examines the dependence between the marginal variables
through copula-based techniques and further explores the distributional
properties of concomitants of order statistics arising from the generalized
Morgenstern-type bivariate exponential distribution.