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.
The recent development in statistics has made statistical distributions the focus of researchers in the process of compensating for some distribution parameters with fixed values and obtaining a new distribution, in this study, the distribution of Kumaraswamy was studied from the constant distributions of the two parameters. The characteristics of the distribution were discussed through the presentation of the probability density function (p.d.f), the cumulative distribution function (c.d.f.), the ratio of r, the reliability function and the hazard function. The parameters of the Kumaraswamy distribution were estimated using MLE, ME, LSEE by using the simulation method for different sampling sizes and using preli
... Show MoreGypsum is one of the important construction materials in Iraq in plastering surfaces and gypsum board , the ability of gypsum to give a comfortable an aesthetic ambiance as a construction material increase the need of gypsum , The particle size , total surface area and particle size distribution were factors affecting plaster properties used for construction properties . In this study gypsum paste was used with different mixing ratios of particle size and studied the physical properties of these types of pastes named (standard consistency ,setting time ,density) and compressive strength . The results showed that the water to gypsum ratio increased with increasing the fineness of the gypsum to (0.75%) and the setting time to the maxi
... Show MoreBixSb2-xTe3 alloys with different ratios of Bi (x=0, 0.1, 0.3, 0.5, and 2) have been prepared, Thin films of these alloys were prepared using thermal evaporation method under vacuum of 10-5 Torr on glass substrates at room temperature with different deposition rate (0.16, 0.5, 0.83) nm/sec for thickness (100, 300, 500) respectively. The X–ray diffraction measurements for BixSb2-xTe3 bulk and thin films indicate the polycrystalline structure with a strong intensity of peak of plane (015) preferred orientation with additional peaks, (0015) and (1010 ) reflections planes, which is meaning that all films present a very good texture along the (015) plane axis at different intensities for each thin film for different thickness. AFM measureme
... Show MoreRecently, emulgel has emerged as one of the most interesting topical preparations in the field of pharmaceutics. In this research clotrimazole was formulated as topically applied emulgel ; different formulas were prepared. The prepared emulgels were evaluated for their physical appearance , rheological behaviour , and in vitro drug release . The influence of the type of gelling agent (carbopol 934 and methyl cellulose), the concentration of both the emulsifying agent (2% and 4% w/w of mixture of span 20 and tween 20) and the oil phase (5% and 7.5% w/w of liquid paraffin) and the type of oil phase (liquid paraffin and cetyl alcohol), on the drug release from the prepared emulgels was invest
... Show MoreThis research of using Feldspar in the production self compacting concrete (SCC) ( 5,10,15 )% as partial replacement by weight of cement .In this research some of fresh properties of SCC ( slump flow used V-funnel test and filling ability used ( U- box test ) for concrete mixes and also some of the harden properties of SCC ( compressive and flexural tests ). The research results showed that negative effect of Feldspar on the fresh properties of self compacting concrete but the positive effect of Feldspar on the harden properties of self compacting concrete .
To achieve sustainability in the field of civil engineering, there has become a great interest in developing reactive powder concrete RPC through the use of environmentally friendly materials to reduce the release of CO2 gas produced from cement factories as well as contribute to the recycling of industrial wastes that have a great impact on environmental pollution.
In this study, reactive powder concrete was prepared using total binder content of 800 kg/m3, water to binder ratio (0.275), and micro steel fibers 1% by volume of concrete. The experimental program included replacing fly ash with (8, 12, 16) % by cement weight to find the optimal ratio, which achieved the best mechanical proper
... Show MoreThe present research had dealt with preparing bars with the length of about (13 cm) and adiametar of (1.5 cm) of composite materials with metal matrix represented by (Al-Cu-Mg) alloy cast enforced by (ZrO2) particles with chosen weight percentages (1.5, 2.5 ,3.5, 5.5 %). The base cast and the composite materials were prepared by casting method by uses vortex Technique inorder to fix up (ZrO2) particles in homogeneous way on the base cast. In addition to that, two main groups of composite materials were prepared depending on the particles size of (ZrO2) , respectively. &n
... Show MoreThe products of composites material are very sesetive to many variables, such as manufacturing process, additive materials, …. etc. Filler or additive plays a major role to determine the formation of the properties and behavior of the composites. In this study, polyethylene terephthalate-based compounds were produced and characterized. The work is concerned to prepare samples of Polyethylene terephthalate (PET) - zinc-ferrite (ZnFe2O4) with different addition ratio as zinc-ferrite (1, 2, 5, 10, 15 and 20) wt% obtained from mixing the solution with a hot pressing method applied under optimum conditions. The densities of the composites for all samples were calculated. Through the work the diffusion of zinc-ferrite i
... Show Morepriorities of materials research due to their promising properties, especially in the field of thermoelectricity. The efficiency or performance of thermoelectric devices is expressed in terms of the thermoelectric figure-of-merit (ZT) – a standard indicator of a material’s thermoelectric properties for use in cooling systems. The evaluation of ZT is principally determined by the thermoelectric characteristics of the nanomaterials. In this paper, a set of investigative computations was performed to study the thermoelectric properties of monolayer TMDCs according to the semiclassical treatment of the Boltzmann transport equation. It was confirmed that the thermoelectric properties of 2D materials can be greatly improved compared with thei
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