This paper introduces a novel non-classical probability distribution, termed the Logistic Map distribution, which is constructed by transforming a polynomial function derived from the second iteration of the logistic map. The logistic map a well-known discrete-time dynamical system has been extensively employed in diverse scientific domains, including population dynamics (to model bounded growth under environmental constraints), physics (to study nonlinear dynamics and deterministic chaos), and economics (to represent complex, nonlinear patterns in financial and economic time series). The proposed distribution is fully characterized by two parameters: a scale parameter and a shape parameter, with the constraint ensuring the non-negativity and integrability of the density. Within this valid parameter space, we rigorously derive and establish a comprehensive suite of statistical properties. These include the probability density function, cumulative distribution function, reliability (survival) function, and hazard (failure rate) function. Furthermore, we obtain analytical expressions for key descriptive measures such as the mode and median, as well as for higher-order characteristics including the moment generating function, factorial moment generating function, and characteristic function. The proposed distribution most closely application field in materials science specifically, the statistical modeling of particle or grain size distributions in industrial powder processing, metallurgy, and pharmaceutical manufacturing. The primary objective of this study is to formalize a new family of probability distributions grounded in the mathematical framework of dynamical systems, specifically leveraging the logistic function commonly encountered in differential and difference equations. By doing so, we bridge concepts from nonlinear dynamics and classical statistical theory. The secondary aim is to conduct a thorough investigation of the distribution’s mathematical structure and statistical behavior, thereby establishing its potential utility for modeling bounded, non-negative random phenomena in applied fields such as reliability engineering, survival analysis, and environmental statistics.
<p>Currently, breast cancer is one of the most common cancers and a main reason of women death worldwide particularly in<strong> </strong>developing countries such as Iraq. our work aims to predict the type of tumor whether benign or malignant through models that were built using logistic regression and neural networks and we hope it will help doctors in detecting the type of breast tumor. Four models were set using binary logistic regression and two different types of artificial neural networks namely multilayer perceptron MLP and radial basis function RBF. Evaluation of validated and trained models was done using several performance metrics like accuracy, sensitivity, specificity, and AUC (area under receiver ope
... Show MoreThe last few years witnessed great and increasing use in the field of medical image analysis. These tools helped the Radiologists and Doctors to consult while making a particular diagnosis. In this study, we used the relationship between statistical measurements, computer vision, and medical images, along with a logistic regression model to extract breast cancer imaging features. These features were used to tell the difference between the shape of a mass (Fibroid vs. Fatty) by looking at the regions of interest (ROI) of the mass. The final fit of the logistic regression model showed that the most important variables that clearly affect breast cancer shape images are Skewness, Kurtosis, Center of mass, and Angle, with an AUCROC of
... Show MoreCongenital anomalies commonly occur in humans, possibly visible. If these anomalies appear in visible parts in human body such as face, hands and feet. They may only appear after utilizing a number of special tests in order to show by means of the anomalies that occur in the internal organs of the body such as heart, stomach and kidneys.
Research data have comprised accessible information in the anomalies birth statistics form situated of Health and Life Statistics section at the Ministry of Health and environment, where the number of anomalies births involved in the study (2603 anomalies birth) in Iraq, except Kurdistan region, at 2015. A two way-response logistic regression analysis h
... Show MorePhysics and applied mathematics form the basis for understanding natural phenomena using differential equations depicting the flow in porous media, the motion of viscous liquids, and the propagation of waves. These equations provide a thorough study of physical processes, enhancing the understanding of complex applications in engineering, technology, and medicine. This paper presents novel approximate solutions for the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational iteration method and the optimal variational iteration method. The variational iteration method is effectively developed by adding a control paramete
... Show MoreThe present study aims to show the importance of ESL reading ability in acquiring English as a second language. The study involves 92 college students (males and females) from the Department of English at Nizwa College of Applied Sciences, Sultanate of Oman. They represent two groups, the foundation year students and the first year English majors. A number of tests were used to measure students’ overall proficiency in English as well as their reading ability (i.e., the ability to contribute to the main idea of the text, scanning, skimming, to derive word meanings from context, to use a dictionary to find meanings, definitions, to identify prefixes, antonyms and synonyms). Students’ ability to read was correlated to their proficiency
... Show MoreThis work aims to provide a statistical analysis of metal removal during the Magnetic Abrasive Finishing process (MAF) and find out the mathematical model which describes the relationship between the process parameters and metal removal, also estimate the impact of the parameters on metal removal. In this study, the single point incremental forming was used to form the truncated cone made of low carbon steel (1008-AISI) based on the Z-level tool path. Then the finishing was accomplished using a magnetic abrasive process based on the Box-Behnken design of the experiment using Minitab 17 software was used to finish the surface of the formed truncated cone. The influences of different parameters (feed rate, machining step s
... Show MoreThe auditory system can suffer from exposure to loud noise and human health can be affected. Traffic noise is a primary contributor to noise pollution. To measure the noise levels, 3 variables were examined at 25 locations. It was found that the main factors that determine the increase in noise level are traffic volume, vehicle speed, and road functional class. The data have been taken during three different periods per day so that they represent and cover the traffic noise of the city during heavy traffic flow conditions. Analysis of traffic noise prediction was conducted using a simple linear regression model to accurately predict the equivalent continuous sound level. The difference between the predicted and the measured noise shows that
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