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.
Abstract
This study was conducted by using soil map of LD7 project to interpret the
distribution and shapes of map units by using the index of compaction as an
index of map unit shape explanation. Where there were wide and varied
ranges of compaction index of map units, where the maximum value was
0.892 for MF9 map unit and the lower value was 0.010 for same map unit.
MF9 has wide range appearance of index of compaction after those indices
were statistically analyzed by using cluster analysis to group the similar
ranges together to ease using their values, so the unit MF9 was considered as
key map unit that appears in the soils of LD7 project which may be used to
expect another map units existence in area of
significant bits either in the spatial domain or frequency domain sequentially or pseudo
randomly through the cover media (Based on this fact) statistical Steganalysis use different
techniques to detect the hidden message, A proposed method is suggested of a stenographic
scheme a hidden message is embedded through the second least significant bits in the
frequency domain of the cover media to avoid detection of the hidden message through the
known statistical Steganalysis techniques.
This research is a theoretical study that deals with the presentation of the literature of statistical analysis from the perspective of gender or what is called Engendering Statistics. The researcher relied on a number of UN reports as well as some foreign sources to conduct the current study. Gender statistics are defined as statistics that reflect the differences and inequality of the status of women and men overall domains of life, and their importance stems from the fact that it is an important tool in promoting equality as a necessity for the process of sustainable development and the formulation of national and effective development policies and programs. The empowerment of women and the achievement of equality between men and wome
... Show MoreSecurity concerns in the transfer of medical images have drawn a lot of attention to the topic of medical picture encryption as of late. Furthermore, recent events have brought attention to the fact that medical photographs are constantly being produced and circulated online, necessitating safeguards against their inappropriate use. To improve the design of the AES algorithm standard for medical picture encryption, this research presents several new criteria. It was created so that needs for higher levels of safety and higher levels of performance could be met. First, the pixels in the image are diffused to randomly mix them up and disperse them all over the screen. Rather than using rounds, the suggested technique utilizes a cascad
... Show MoreIt is necessary to examine the nature of the Turkish position and what Turkey seeks to achieve at the international, regional and Iraqi levels. Or is this external role an expression of foreign policy and has not yet reached the level of maturity that reaches the stage of strategy? The answer to this question is the essence of research in the Turkish role. The answer to this question requires the realization of the elements and pillars that guarantee Turkey's continuity and survival. Continuity is a cornerstone of the strategy. The continuity of the role and its interaction with the event and the ability to employ multiple alternatives are what qualify the state to describe its politics. The external strategy has evolved into. In order t
... Show MoreEarth’s climate changes rapidly due to the increases in human demands and rapid economic growth. These changes will affect the entire biosphere, mostly in negative ways. Predicting future changes will put us in a better position to minimize their catastrophic effects and to understand how humans can cope with the new changes beforehand. In this research, previous global climate data set observations from 1961-1990 have been used to predict the future climate change scenario for 2010-2039. The data were processed with Idrisi Andes software and the final Köppen-Geiger map was created with ArcGIS software. Based on Köppen climate classification, it was found that areas of Equator, Arid Steppes, and Snow will decrease by 3.9 %, 2.96%, an
... Show MoreIn digital images, protecting sensitive visual information against unauthorized access is considered a critical issue; robust encryption methods are the best solution to preserve such information. This paper introduces a model designed to enhance the performance of the Tiny Encryption Algorithm (TEA) in encrypting images. Two approaches have been suggested for the image cipher process as a preprocessing step before applying the Tiny Encryption Algorithm (TEA). The step mentioned earlier aims to de-correlate and weaken adjacent pixel values as a preparation process before the encryption process. The first approach suggests an Affine transformation for image encryption at two layers, utilizing two different key sets for each layer. Th
... Show MoreThe effect of the initial pressure upon the laminar flame speed, for a methane-air mixtures, has been detected paractically, for a wide range of equivalence ratio. In this work, a measurement system is designed in order to measure the laminar flame speed using a constant volume method with a thermocouples technique. The laminar burning velocity is measured, by using the density ratio method. The comparison of the present work results and the previous ones show good agreement between them. This indicates that the measurements and the calculations employed in the present work are successful and precise
Soil pH is one of the main factors to consider before undertaking any agricultural operation. Methods for measuring soil pH vary, but all traditional methods require time, effort, and expertise. This study aimed to determine, predict, and map the spatial distribution of soil pH based on data taken from 50 sites using the Kriging geostatistical tool in ArcGIS as a first step. In the second step, the Support Vector Machines (SVM) machine learning algorithm was used to predict the soil pH based on the CIE-L*a*b values taken from the optical fiber sensor. The standard deviation of the soil pH values was 0.42, which indicates a more reliable measurement and the data distribution is normal.
This article investigates how an appropriate chaotic map (Logistic, Tent, Henon, Sine...) should be selected taking into consideration its advantages and disadvantages in regard to a picture encipherment. Does the selection of an appropriate map depend on the image properties? The proposed system shows relevant properties of the image influence in the evaluation process of the selected chaotic map. The first chapter discusses the main principles of chaos theory, its applicability to image encryption including various sorts of chaotic maps and their math. Also this research explores the factors that determine security and efficiency of such a map. Hence the approach presents practical standpoint to the extent that certain chaos maps will bec
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