Exponential Distribution Research Articles

The Transformed MG-Extended Exponential Distribution: Properties and Applications

Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution’s parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions.

On the Poisson-transmuted exponential distribution and its application to frequency of claim in actuarial science

This study proposes a new discrete distribution in the mixed Poisson paradigm to obtain a distribution that provides a better fit to skewed and dispersed count observation with excess zero. The cubic transmutation map is used to extend the exponential distribution, and the obtained continuous distribution is assumed for the parameter of the Poisson distribution. Various moment-based properties of the new distribution are obtained. The Nelder-Mead algorithm provides the fastest convergence iteration under the maximum likelihood estimation technique. The shapes of the proposed new discrete distribution are similar to those of the mixing distribution. Frequencies of insurance claims from different countries are used to assess the performance of the new proposition (and its zero-inflated form). Results show that the new distribution outperforms other competing ones in most cases. It is also revealed that the natural form of the new distribution outperforms its zeroinflated version in many cases despite having observations with excess zero counts.

A Study on One-Parameter Entropy-Transformed Exponential Distribution and Its Application

This study presents the Entropy-Transformed Exponential Distribution (EnTrED), in an attempt to enhancing the flexibility and applicability of the traditional exponential distribution. The study explores the statistical properties of the EnTrED, including mode, quantile function, reliability, moments, and hazard function. The parameters of the distribution were estimated using maximum likelihood estimation, and the stability of these estimates was thoroughly evaluated through extensive Monte Carlo simulation. The simulation results demonstrated that the maximum likelihood estimates of the model parameters were well-behaved. Additionally, Empirical assessments against alternative distributions underscores the robustness of the EnTrED as a superior model for analyzing life data.

Suspicious behaviour detection in multilayer social networks using PF-KMA and SS-GAE techniques

Multilayer Social networks are an important part of human life to interact on different networks at the same time. Due to the openness of such networks, they become a platform for spammers to spread malicious behaviors. Hence, there is an urgent need for effective detection of malicious behaviors; thereby, enabling the networks to take mitigation actions to decrease the possibility to reward such activities. Detection of suspicious behaviors in previous works is challenging due to the problems of community detection, the large amount of feature corruption, and memory requirements. Thus, to deal with such problems, in this paper, an efficient clustering-based detection of malicious users in multilayer social networks is proposed. Initially, the input dataset is pre-processed and used for Exponential Distribution based Erdős–Rényi based graph construction. From the graph structure, two types of data, such as user representations and graph features are extracted for graph encoding using the Soft Sign activated Graph Auto Encoder model. Then, the decoding is done to predict the information diffusion level, thereby, ranking the users using the Laplace Regularization technique. Then, the ranked users are clustered into different groups using the Pareto Front based K-Means Clustering Algorithm technique. Finally, the experimental results were analyzed to demonstrate the efficacy of the proposed model to detect malicious users in multilayer social networks.

Linear Combination of Order Statistics Moments from Log-Extended Exponential Geometric Distribution with Applications to Entropy

Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs.

A Parametric Cox Proportional Hazard Model with Application

Survival analysis has become integral to clinical studies, especially in emerging diseases and terminal ailments. This study focused on improving the popular Cox PH model. The new method developed is a parametric type, incorporating the hazard rate of the exponential distribution. It was noted that though the functional form of the Cox PH model was altered, the assumptions were upheld. Additionally, the new model parameters were estimated using the same maximum partial likelihood as the Cox model. Data on the survival times of 137 patients who underwent bone marrow transplants were deployed, and the proposed parametric Cox PH model proved superior to the Cox PH model.

From Malthusian stagnation to modern economic growth: a swarm-intelligence perspective

The correlation between decentralized decision-making and swarm intelligence has emerged as a significant subject within self-organization phenomena. Here, we demonstrate that, if an exponential probability distribution of income emerges in a decentralized economic system, then the total income of all agents can be represented by an aggregate production function, in which the technology factor precisely aligns with the information content inherent in the event of decentralized decision-making by all agents. In particular, for sufficiently large population sizes, the emergence of this technology factor enables the income per capita to increase with the population size, akin to a manifestation of swarm intelligence. More importantly, we find that an exponential probability distribution of income can be generated within a peer-to-peer economy governed by specific game rules, characterizing a decentralized-decision economic system. Building upon this discovery, we propose a swarm-intelligence explanation to elucidate the transition from thousands of years of Malthusian stagnation to modern economic growth.

Reliability inference based on inverted exponentiated Rayleigh lifetime distribution under unified hybrid censored scheme

In this study, we investigated the Inverted Exponentiated Rayleigh Distribution (IERD), a significant and efficient continuous lifetime distribution commonly applied in lifespan research. Our focus was on estimating unknown parameters for a two-parameter inverted exponentiated Rayleigh distribution using unified hybrid censored data. We considered both maximum likelihood and Bayesian estimation approaches. Specifically, we employed the Gibbs within Metropolis–Hastings samplers method to develop approximate Bayes estimators utilizing informative and non-informative priors, along with symmetric and asymmetric loss functions. In addition, we utilized Markov chain Monte Carlo (MCMC) samples to derive maximum posterior density credible intervals. Simulation experiments were conducted to assess the efficacy of the proposed methodologies, and actual data analysis was performed to validate the proposed estimators.

37‐4: Degradation Analysis on Li‐doped Organic Charge Generation Layer

Understanding degradation of charge generation layer (CGL) is uprising issue for efficient and stable tandem devices. Here, we explored how the electrical characteristics of Li‐doped CGL device change according to different stress conditions comprehensively and found out thermal stress affects more severely than electrical stress via capacitance‐voltage and temperature‐dependent current density‐voltage measurements. The exponential trap distribution model analysis and Poisson and drift‐diffusion simulation informed that the degradation of electrical properties is attributed to Li diffusion and actual thermal diffusion of Li was experimentally observed by XPS depth

Advancing Solar Energetic Particle Event Prediction through Survival Analysis and Cloud Computing. I. Kaplan–Meier Estimation and Cox Proportional Hazards Modeling

Solar energetic particles (SEPs) pose significant challenges to technology, astronaut health, and space missions. This initial paper in our two-part series undertakes a comprehensive analysis of the time to detection for SEPs, applying advanced statistical techniques and cloud-computing resources to deepen our understanding of SEP event probabilities over time. We employ a range of models encompassing nonparametric, semiparametric, and parametric approaches, such as the Kaplan–Meier estimator and Cox Proportional Hazards models. These are complemented by various distribution models—including exponential, Weibull, lognormal, and log-logistic distributions—to effectively tackle the challenges associated with “censored data,” a common issue in survival analysis. Employing Amazon Web Services and Python’s “lifelines” and “scikit-survival” libraries, we efficiently preprocess and analyze large data sets. This methodical approach not only enhances our current analysis, but also sets a robust statistical foundation for the development of predictive models, which will be the focus of the subsequent paper. In identifying the key determinants that affect the timing of SEP detection, we establish the vital features that will inform the machine-learning (ML) techniques explored in the second paper. There, we will utilize advanced ML models—such as survival trees and random survival forests—to evolve SEP event prediction capabilities. This research is committed to advancing space weather, strengthening the safety of space-borne technology, and safeguarding astronaut health.

Transient Analysis of Two-Dimensional State M/M/2 Queueing Model with Multiple Vacations, Catastrophes and Feedback

This study obtains transient solution of two-dimensional state Markovian queueing model with homogenous servers, multiple vacations, catastrophes and feedback. Inter-arrival and service times follow an exponential distribution with parameters ? and ?, respectively. Units are ejected from the system when catastrophes occur. Servers get deactivated for a moment and are ready for service when new units arrive. Occurrence of catastrophes follows Poisson distribution with rate. After receiving the service, the units either exit or rejoin the system immediately at the early end of the queue; this is known as ?feedback?. Laplace transform approach has been used to find transient solution and discover some quantifiable results.. KEYWORDS :Markovian queue, Laplace transform, Multiple vacations, Catastrophes, Feedback

A two Identical Unit Cold Standby System with two Repairmen and Correlated Failure and Repair Times

The paper deals with the stochastic analysis of a two identical unit cold standby system model. As soon as a unit fails it is attended first by assistant repairman, who completes its repair to make it as good as new with fixed known probability p. Otherwise, with probability q( =1-p), the unit repaired by assistant repairman goes to expert repairman so as to make it as good as new. Both the repairmen are always available with the system and they work their jobs simultaneously. The failure time and repair time by assistant repairman are correlated random variables having their joint distribution as Bivariate exponential. Various measures of system effectiveness useful to system designers and operation managers are obtained by using regenerative point technique. The MTSF and steady state profit have also been studied through graphs in respect of parameter alpha for three different values of repair rate by expert repairman and two different values of correlation coefficient between failure and repair times and important conclusions are drawn.. KEYWORDS :Bivariate exponential distribution, Mean time to system failure (MTSF), Regenerative point, Laplace transform.

Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution with Fuzzy Data

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information availableisin the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function linksequalimportance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently

Inter-turn intervals in Paramecium caudatum display an exponential distribution

ABSTRACT In navigating to a better location, mobile organisms in diverse taxa change directions of travel occasionally, including bacteria, archaea, single-celled eukaryotes, and small nematode worms such as Caenorhabditis elegans. In perhaps the most common form of goal-orientated movement, the rate of such turns is adjusted in all these taxa to ascend (or descend) a chemical gradient. Basically, the rate of turns is reduced when the movement results in better conditions. In the bacterium Escherichia coli and in C. elegans, the turns are generated by random-rate processes, in which the probability of a turn occurring is constant at every moment. This is evidenced by a distribution of inter-turn intervals that has an exponential distribution. For the first time, we examined the distribution of inter-turn intervals in the single-celled eukaryote, Paramecium caudatum, in a class exercise for first-year university students. We found clear evidence for an exponential distribution of inter-turn intervals, implying a random-rate process in generating turns in Paramecium. The exercise also shows that university laboratory classes can be used to generate scientific data to address research questions whose answers are as yet unknown.

DIVERSITY AND REGENERATION OF WOODY PLANTS OF LOGONE BIRNI FLOODPLAIN VEGETATION IN THE FAR NORTH REGION OF CAMEROON

This study aims to contribute to the conservation and sustainable management of the Logone-Birni floodplains in Cameroon. In total, 27 plots of 100 m x 100 m plots of were laid out in 3 land use types (protected area, grazing area and agricultural area). Within each plot, all woody individuals having ≥ 10 cm circumference at breast height (> 1.3 m) were identified, and all the stems with a circumference ≤ 10 cm were considered as seedlings. A total of 43 timber species belonging to 35 genera and 21 families were harvested. Shannon-Weaver diversity ranged from 1.77-2.39 and the Pielou equitability index from 0.84-0.88 with low values in agricultural areas and higher values in protected and grazing areas. The distribution of stems according to diameter and height showed that all stands exhibit classic exponential decay distribution ‘‘L’’ or ‘‘J’’ inverted, reflecting the predominance of individuals with small diameters. The regeneration rates of the stand vary from 0.81 to 51.56%, indicating a difficult regeneration due partly to anthropogenic activities. It also appears that given the low diversity and the difficult regeneration of the stand, it is important, even crucial, to manage this plain to ensure the conservation and sustainable management of the biological resources that it hosts.

Performance Assessment of Natural Survivor Method-Based Metaheuristic Optimizers in Global Optimization and Engineering Design Problems

This study presents the comparative performance analysis of Natural Survivor Method (NSM)-based algorithms in solving the IEEE CEC 2022 test suite benchmark problems and four real-world engineering design problems. Three different variants (Case1, Case2, Case3) of the NSM-TLABC, NSM-SFS and NSM-LSHADE-SPACMA algorithms were used in the study. The data obtained from the experimental studies were statistically analyzed using Friedman and Wilcoxon signed-rank tests. Based on the Friedman test results, NSM-LSHADE-SPACMA_Case2 showed the best performance with an average Friedman score of 3.96. The Wilcoxon signed-rank test showed that NSM-LSHADE-SPACMA_Case2 outperformed its competitors in 13 out of 16 experiments, achieving a success rate of 81.25%. NSM-LSHADE-SPACMA_Case2, which was found to be the most powerful of the NSM-based algorithms, is used to solve cantilever beam design, tension/compression spring design, pressure vessel design and gear train design problems. The optimization results are also compared with eight state-of-the-art metaheuristics, including Rime Optimization Algorithm (RIME), Nonlinear Marine Predator Algorithm (NMPA), Northern Goshawk Optimization (NGO), Kepler Optimization Algorithm (KOA), Honey Badger Algorithm (HBA), Artificial Gorilla Troops Optimizer (GTO), Exponential Distribution Optimization (EDO) and Hunger Games Search (HGS). Given that all results are together, it is seen that NSM-LSHADE-SPACMA_Case2 algorithm consistently produced the best results for the global and engineering design problems studied.

Multiple dependent state repetitive sampling plan odd log-logistic generalized exponential distribution with application to beverage product’s carbon dioxide pressure and concentration

Multiple dependent state repetitive sampling plan odd log-logistic generalized exponential distribution with application to beverage product’s carbon dioxide pressure and concentration

Statistical reliability analysis of marine systems with varied levels of redundancy

In designing autonomous vessels for long-duration independent operation, maintaining the performance of machinery systems without human intervention is a key challenge. Designers are faced with a range of potential system architecture choices but have little guidance on which will be optimal. Working only with high-reliability components can increase the probability of completing a voyage successfully, though the availability of such components may be limited. Alternatively, designers can select a redundant architecture to provide options for reconfiguration if a component fails during a voyage, such architectures typically have weight, space, and cost implications. This work presents a parametric exploration of the probability of system failures over time under different architectures. The reliability of individual components is expressed through exponential probability distributions and the weight of each component is approximated. Two systems are presented and the effectiveness of various architectures for both systems is compared. A simple design penalty function is also tracked to capture the different architectures’ weight and implication number of components. From this study optimal architectures for long-term autonomous missions are proposed.

Monitoring the inverted exponentiated half logistic quantiles under the adaptive progressive type II hybrid censoring scheme

Numerous studies have solved the problem of monitoring statistical processes with complete samples. However, censored or incomplete samples are commonly encountered due to constraints such as time and cost. Adaptive progressive Type II hybrid censoring is a novel method with the advantages of saving time and improving efficiency. On the basis of this scheme, the problem of monitoring a downward shift in the quantiles of the inverted exponentiated half logistic distribution is considered. The conventional Shewhart control chart is insensitive to detect quantile shifts from faulty data processes that exhibit deviations from normality or symmetry. To overcome this limitation, Bootstrap control charts combining with the exponentially weighted moving average method based on the Bayesian estimation and maximum likelihood estimation are proposed, respectively. They are compared with the conventional Shewhart control chart via average run length through Monte-Carlo simulations. Finally, a real dataset related to the tensile strength of carbon fibers is employed to demonstrate the ascendancy of the Bootstrap control charts.

Geometrical properties of three-dimensional crossed nanowire networks

Three-dimensional interconnected nanowire networks have recently attracted notable attention for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic and spintronic applications, and for the design of new hardware neuromorphic computing architectures. However, the complex branching of these nanowire networks makes it challenging to investigate these 3D nanostructured systems theoretically. Here, we present a theoretical description and simulations of the geometric properties of these 3D interconnected nanowire networks with selected characteristics. Our analysis reveals that the nanowire segment length between two crossing zones follows an exponential distribution. This suggests that shorter nanowire segments have a more pronounced influence on the nanowire network properties compared to their longer counterparts. Moreover, our observations reveal a homogeneous distribution in the smallest distance between the cores of two crossing nanowires. The results are highly reproducible and unaffected by changes in the nanowire network characteristics. The density of crossing zones and interconnected nanowire segments is found to vary as the square of the nanowire density multiplied by their diameter, further multiplied by a factor dependent on the packing factor. Finally, densities of interconnected segments up to 1013cm−2 can be achieved for 22-µm-thick nanowire networks with high packing factors. This has important implications for neuromorphic computing applications, suggesting that the realization of 1014 interconnections, which corresponds to the approximate number of synaptic connections in the human brain, is achievable with a nanowire network of about 10cm2. Published by the American Physical Society 2024