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Artykuły w czasopismach na temat „Statistical formula”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Lippi, U., M. S. Graziani, F. Manzato, and M. Schinella. "The Friedewald formula: statistical acrobatics?" Clinical Chemistry 32, no. 5 (1986): 909–10. http://dx.doi.org/10.1093/clinchem/32.5.909.

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Gao, Yan Qiang, and Wen Feng Liu. "Statistical Analysis of Fundamental Periods of Frame Structures." Applied Mechanics and Materials 226-228 (November 2012): 1174–80. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1174.

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The differences of empirical formulas of China, the United States, Japan, and Europe for estimating the fundamental periods of frame structures are investigated. Summing up paradigms of the empirical formulas from the above representation countries, the paradigm formulas expressed as single-variable exponential type, single-variable linear type, and multi-variable non-linear type. Using statistical data of 36 groups of the measured fundamental period for least-squares regression analysis, and the effect of fitting regression formula is judged by the norm of relative error ‖δ‖2, the norm of roo

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3

Gao, Yan Qiang, and Wen Feng Liu. "Statistical Analysis of Fundamental Periods of Frame-Shear Wall Structures." Applied Mechanics and Materials 174-177 (May 2012): 2071–78. http://dx.doi.org/10.4028/www.scientific.net/amm.174-177.2071.

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The differences of empirical formulas of China, United States, Japan, and Europe for estimating the fundamental periods of frame-shear wall structures are investigated. Summing up paradigms of the empirical formulas from the above representation countries, the paradigm formulas expressed as single-variable exponential type, single-variable linear type, and multi-variable non-linear type. Using statistical data of 88 groups of the measured fundamental period for least-squares regression analysis, and the effect of fitting regression formula is judged by the norm of relative error‖δ‖2 , the norm

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4

Boudh-Hir, M. E., and G. A. Mansoori. "Statistical mechanics basis of Macleod's formula." Journal of Physical Chemistry 94, no. 21 (1990): 8362–64. http://dx.doi.org/10.1021/j100384a068.

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5

Tajudeen, ADENIRAN Adefemi, OJO Johnson Funminiyi, FAWEYA Olanrewaju, and BALOGUN Kayode. "Statistical Measures of Location: Mathematical Formula Versus Geometric Approach." Academic Journal of Applied Mathematical Sciences, no. 67 (July 10, 2020): 145–52. http://dx.doi.org/10.32861/ajams.67.145.152.

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Graphical method and mathematical formula are the two approaches for estimating measures of location. Understanding of many instructors of introductory statistics classes are: mean cannot be graphically determined and numerical (formula) approach is more precise than geometrical technique. Contrary to their understanding, this study estimate mean of a dataset geometrically (from histogram) by determining the centroid of histogram drawn from such data set. In addition, we also make known that mathematical formulas for mean, median and mode were derived geometrically (either from ogive or histog

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6

Niedbala, Raymond S., and Keith J. Schray. "In Reply: The Friedewaid Formula: Statistical Acrobatics?" Clinical Chemistry 32, no. 5 (1986): 910–11. http://dx.doi.org/10.1093/clinchem/32.5.910.

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7

Debnath, Shyamal, та Bijoy Das. "Statistical Convergence of Order α for Complex Uncertain Sequences". Journal of Uncertain Systems 14, № 02 (2021): 2150012. http://dx.doi.org/10.1142/s1752890921500124.

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In this paper, we introduce convergence concepts namely, statistical convergence of order [Formula: see text], statistical convergence of order [Formula: see text] almost surely, statistical convergence of order [Formula: see text] in measure, statistical convergence of order [Formula: see text] in mean, statistical convergence of order [Formula: see text] in distribution in complex uncertain theory. We also investigate some relationships among them.

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8

Jiang, Rong, Zhao Yang, Song Chen, Ying Yuan, and Liang Liu. "Statistical Characteristics of Stress Changes in Tunnel Surrounding Rock Based on Random Discrete Variability of Geotechnical Materials." Applied Sciences 13, no. 24 (2023): 12986. http://dx.doi.org/10.3390/app132412986.

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In the construction of underground engineering, the determination of surrounding rock stresses has important theoretical significance for the design of tunnel structure reliability. In this paper, the nonlinear criterion is introduced to modify and improve the friction resistance in the calculation formula of Bierbaumer’s loose surrounding rock stresses, and the improved application is carried out in view of the situation of composite formation. Due to the variability and discreteness of geotechnical parameters, combined with engineering examples, Monte Carlo random sampling is carried out for

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9

ROSSO, OSVALDO A., LUCIANA DE MICCO, HILDA A. LARRONDO, MARÍA T. MARTÍN, and ANGEL PLASTINO. "GENERALIZED STATISTICAL COMPLEXITY MEASURE." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 775–85. http://dx.doi.org/10.1142/s021812741002606x.

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A generalized Statistical Complexity Measure (SCM) is a functional that characterizes the probability distribution P associated to the time series generated by a given dynamical system. It quantifies not only randomness but also the presence of correlational structures. We review here several fundamental issues in such a respect, namely, (a) the selection of the information measure [Formula: see text]; (b) the choice of the probability metric space and associated distance [Formula: see text]; (c) the question of defining the so-called generalized disequilibrium [Formula: see text]; (d) the ade

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10

LUOR, DAH-CHIN. "STATISTICAL PROPERTIES OF LINEAR FRACTAL INTERPOLATION FUNCTIONS FOR RANDOM DATA SETS." Fractals 26, no. 01 (2018): 1850009. http://dx.doi.org/10.1142/s0218348x18500093.

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Let [Formula: see text] be an integer greater than or equal to [Formula: see text] and let [Formula: see text] be numbers with [Formula: see text]. Denote that [Formula: see text] is the interval [Formula: see text] and [Formula: see text] is a set of points. Suppose that [Formula: see text] is a random perturbation of [Formula: see text] for [Formula: see text], and we set [Formula: see text]. Let [Formula: see text] and [Formula: see text] be linear fractal interpolation functions on [Formula: see text] corresponding to the set of points [Formula: see text] and [Formula: see text], respectiv

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11

Connell, Benjamin J., and Jack X. Kane. "Comparison of the Kane formula with existing formulas for intraocular lens power selection." BMJ Open Ophthalmology 4, no. 1 (2019): e000251. http://dx.doi.org/10.1136/bmjophth-2018-000251.

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ObjectiveTo compare the accuracy of a new intraocular lens (IOL) power formula (Kane formula) with existing formulas using IOLMaster, predominantly model 3, biometry (measures variables axial length, keratometry and anterior chamber depth) and optimised lens constants. To compare the accuracy of three new or updated IOL power formulas (Kane, Hill-RBF V.2.0 and Holladay 2 with new axial length adjustment) compared with existing formulas (Olsen, Barrett Universal 2, Haigis, Holladay 1, Hoffer Q, SRK/T).Methods and analysisA single surgeon retrospective case review was performed from patients hav

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12

McClure, Foster D., and Jung K. Lee. "On Determining a 1-Tailed Upper Limit for Future Sample HorRat Values." Journal of AOAC INTERNATIONAL 89, no. 6 (2006): 1650–63. http://dx.doi.org/10.1093/jaoac/89.6.1650.

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Abstract Two formulas were developed for use in computing 1-tailed upper limits for future HorRat values obtained from the collaborative study of materials. One formula is applicable when a future sample HorRat value &lt;inline-formula&gt; &lt;inline-graphic href="inline_eq1.gif"/&gt; &lt;/inline-formula&gt; is computed based on a known concentration (e.g., C spike level and RSDR is the sample relative reproducibility standard deviation) and the other formula is applicable when the true concentration (C) is unknown and a future sample HorRat value &lt;inline-formula

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13

Hu, Tien-Chung. "A Statistical Method of Approach to Stirling's Formula." American Statistician 42, no. 3 (1988): 204. http://dx.doi.org/10.2307/2685005.

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14

Hu, Tien-Chung. "A Statistical Method of Approach to Stirling's Formula." American Statistician 42, no. 3 (1988): 204–5. http://dx.doi.org/10.1080/00031305.1988.10475566.

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15

Boonklurb, Ratinan, Ampol Duangpan, Udomsak Rakwongwan, and Phiraphat Sutthimat. "A Novel Analytical Formula for the Discounted Moments of the ECIR Process and Interest Rate Swaps Pricing." Fractal and Fractional 6, no. 2 (2022): 58. http://dx.doi.org/10.3390/fractalfract6020058.

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This paper presents an explicit formula of conditional expectation for a product of polynomial functions and the discounted characteristic function based on the Cox–Ingersoll–Ross (CIR) process. We also propose an analytical formula as well as a very efficient and accurate approach, based on the finite integration method with shifted Chebyshev polynomial, to evaluate this expectation under the Extended CIR (ECIR) process. The formulas are derived by solving the equivalent partial differential equations obtained by utilizing the Feynman–Kac representation. In addition, we extend our results to

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16

Kou, Jiaojiao, Pingjun Chang, Lei Lin, Zhangliang Li, Yana Fu, and Yun-e. Zhao. "Comparison of the Accuracy of IOL Power Calculation Formulas for Pediatric Eyes in Children of Different Ages." Journal of Ophthalmology 2020 (July 27, 2020): 1–6. http://dx.doi.org/10.1155/2020/8709375.

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Purpose. This study aims to compare the accuracy of five intraocular lens (IOL) power calculation formulas (SRK/T, Hoffer Q, Holladay 1, Haigis, and Holladay 2) for pediatric eyes in children of different ages. Methods. In this prospective study, patients who received cataract surgery and IOL implantation in the capsular bag were enrolled. We compared the calculation accuracy of 5 formulas at 1 month postoperatively and performed subgroup analysis with the patients divided into three groups according to their ages at the time of surgery as follows: group 1 (age ≤ 2 years, 35 eyes), group 2 (2

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17

BANERJEE, S. N., R. K. DAS, and A. K. SARKER. "PROPERTIES OF MESONS IN THE STATISTICAL MODEL." International Journal of Modern Physics A 04, no. 04 (1989): 943–62. http://dx.doi.org/10.1142/s0217751x89000431.

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Within the framework of the statistical model, various properties of mesons are studied. The model which leads to an analytical expression for the number density of quark and antiquark, yields a mass formula of the S state levels of [Formula: see text], [Formula: see text], and [Formula: see text] families. The level spacing between the ground state and a radially excited state in ψ and ϒ families studied in this model reveals interesting relations between the sizes of the particles. With the wave function suggested from the model as an input, magnetic dipoles decays of π and K mesons have bee

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18

Liu, Meng, Dong Chen, Hong-Guang Sun, and Feng Zhang. "Vertical Distribution of Suspended Sediment Concentration in the Unsaturated Jingjiang Reach, Yangtze River, China." Fractal and Fractional 7, no. 6 (2023): 456. http://dx.doi.org/10.3390/fractalfract7060456.

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The Rouse formula and its variants have been widely used to describe the vertical distribution of the sediment concentration in sediment-laden flows in equilibrium. Han’s formula extends the Rouse formula to non-equilibrium regimes, where the diffusive flux is still assumed to be Fickian. The turbulent flow and suspension regimes downstream of a mega-reservoir, e.g., the Three Gorges Reservoir, usually exhibit fractal and unsaturated properties, respectively. To characterize the non-Fickian dynamics of suspended sediment and the non-equilibrium regime in natural dammed rivers, this study propo

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19

Yiğit, M. "Analysis of the reaction Q-value effect using newly evaluated empirical formulas of (n,2n) cross-sections near 14.6MeV." International Journal of Modern Physics E 29, no. 02 (2020): 2050005. http://dx.doi.org/10.1142/s0218301320500056.

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Empirical formulas in determining the cross-sections play an important role at the energies of which there are no experimental data scattered about. The purpose of the present communication is to further improve the formulas of the cross-section of [Formula: see text] reactions at the energies near 14.6[Formula: see text]MeV. A systematics for the evaluation of these cross-sections is studied. We present the empirical formulas based on the statistical theory of nuclear reactions in connection with the compound nucleus. The new empirical formulas are found by using the experimental cross-sectio

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20

Takase, Yasushi, and Nao-Aki Noda. "Convenient and accurate formulas for stress intensity factor distribution of semi-elliptical surface crack." International Journal of Modern Physics B 35, no. 14n16 (2021): 2140002. http://dx.doi.org/10.1142/s0217979221400026.

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In this paper, the stress intensity factor (SIF) formula [Formula: see text] along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution [Formula: see text] is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio [Formula: see text]/[Formula: see text] is focused considering the exact solution [Formula: see text] of an elliptical crack. By applying the least squares method to the ratio [Formula: see text]/[Formula: see text], accurate and convenient formula is

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21

Xie, Ai-Gen, Kun Zhon, De-Lin Zhao, and Yu-Qing Xia. "Formulae for low-energy secondary electron yield from different kinds of emitters as a function of measurable variables." Modern Physics Letters B 31, no. 10 (2017): 1750105. http://dx.doi.org/10.1142/s0217984917501056.

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Based on the characteristics of secondary electron emission and the relationships among parameters of secondary electron yield [Formula: see text] in the low-energy range of [Formula: see text] eV (low-energy [Formula: see text]), the universal formula for low-energy [Formula: see text] as a function of [Formula: see text], [Formula: see text] and maximum [Formula: see text] was deduced, where [Formula: see text] and [Formula: see text] are the incident energies of primary electron and of [Formula: see text], respectively. From the deduced universal formula and experimental low-energy [Formula

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22

ARAKI, HUZIHIRO, and HAJIME MORIYA. "EQUILIBRIUM STATISTICAL MECHANICS OF FERMION LATTICE SYSTEMS." Reviews in Mathematical Physics 15, no. 02 (2003): 93–198. http://dx.doi.org/10.1142/s0129055x03001606.

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We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the equivalence of the KMS condition and the variational principle with a minimal assumption for the dynamics and without any explicit assumption on the potential. Its proof applies to spin lattice systems as well, yielding a vast improvement over known results. All formulations are in terms of a C*-dynamical systems for the Fermion (CAR) algebra [Formula: see text] w

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23

Heckman, Jonathan J. "Statistical inference and string theory." International Journal of Modern Physics A 30, no. 26 (2015): 1550160. http://dx.doi.org/10.1142/s0217751x15501602.

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In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an [Formula: see text]-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a [Formula: see text]-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in [Formula: see text] dimensions. Stability under perturbations to the original inference sc

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24

Morchio, G., and F. Strocchi. "Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering." Reviews in Mathematical Physics 28, no. 01 (2016): 1650001. http://dx.doi.org/10.1142/s0129055x1650001x.

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Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics [Formula: see text] allowing for the existence of Møller operators. We show that (for each scattering channel) [Formula: see text] uniquely identifies, for [Formula: see text], asymptotic dynamics [Formula: see text]; they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the [Formula: see text]-matrix. In view of the application to field theory models, we extend the result to the adiabatic pro

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25

Price, David, Andrew Curtis, and Rachel Wood. "Statistical correlation between geophysical logs and extracted core." GEOPHYSICS 73, no. 3 (2008): E97—E106. http://dx.doi.org/10.1190/1.2890409.

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The precise correlation of extracted core to geophysical borehole logs is often problematic in intervals in which no sufficiently large or distinctive features span the gap between the outer core surface and the borehole wall. This impairs our ability to use techniques that require accurate correlation as a prerequisite (e.g., to develop field-based, upscaling and downscaling relationships of porosity distributions at or below log resolution). We propose a new method for such situations in which we correlate a cascade of statistics of core features with those of image logs taken from the boreh

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26

Han, Shaoyong, Qiang Guo, Kai Yu, Rende Li, Bing He, and Jian-Guo Liu. "Statistical mechanism of passenger mobility behaviors for different transportations." International Journal of Modern Physics C 31, no. 06 (2020): 2050082. http://dx.doi.org/10.1142/s0129183120500825.

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Passengers’ boarding time interval is of great significance for analysis of collective mobility behaviors. In this paper, we empirically investigate the boarding time interval of mobility behaviors based on three large-scale reservation records of passengers traveling by three different types of transportation from a travel agency platform, namely airplane, intercity bus and car rental. The statistical results show that similar properties exist in the passengers’ mobility behaviors, for example, there are similar burstiness [Formula: see text] and memory [Formula: see text] for different time

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27

Alcock-Zeilinger, Judith, Stefan Keppeler, Simon Plätzer, and Malin Sjodahl. "Wigner 6j symbols for SU(N): Symbols with at least two quark-lines." Journal of Mathematical Physics 64, no. 2 (2023): 023504. http://dx.doi.org/10.1063/5.0131538.

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We study a class of [Formula: see text] Wigner 6 j symbols involving two fundamental representations and derive explicit formulas for all 6 j symbols in this class. Our formulas express the 6 j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulas as a first step toward efficiently decomposing [Formula: see text] color structures in terms of group invariants.

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Tsallis, Constantino, and Rute Oliveira. "Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 5 (2022): 053126. http://dx.doi.org/10.1063/5.0090864.

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In the realm of Boltzmann–Gibbs statistical mechanics, there are three well known isomorphic connections with random geometry, namely, (i) the Kasteleyn–Fortuin theorem, which connects the [Formula: see text] limit of the [Formula: see text]-state Potts ferromagnet with bond percolation, (ii) the isomorphism, which connects the [Formula: see text] limit of the [Formula: see text]-state Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism, which connects the [Formula: see text] limit of the [Formula: see text]-vector ferromagnet with self-avoiding random walk in

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29

Benneh, Mensah George. "Saturation Formula for Sample Size Determination in Qualitative Research." Interdisciplinary Journal For Social Sciences (IJFSS) 2025, no. 2 (2025): 201–32. https://doi.org/10.62839/IJFSS.v2025.v02.201-232.

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<strong>Abstract</strong> Determining appropriate sample sizes in qualitative research has traditionally relied on data saturation, lacking predetermined mathematical formulas. Initial efforts by Tullis and Wood introduced basic calculation methods for user experience research, while Yocco proposed preliminary equations for interview-based studies. Balboni further developed these concepts, introducing complexity factors in sample size determination. Building on these foundations, the Benneh-Mensah (BM) Formula integrates study complexity parameters, researcher expertise levels, and statistical

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MOCZURAD, M., J. TYSZKIEWICZ, and M. ZAIONC. "Statistical properties of simple types." Mathematical Structures in Computer Science 10, no. 5 (2000): 575–94. http://dx.doi.org/10.1017/s0960129599002959.

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We consider types and typed lambda calculus over a finite number of ground types. We are going to investigate the size of the fraction of inhabited types of the given length n against the number of all types of length n. The plan of this paper is to find the limit of that fraction when n → ∞. The answer to this question is equivalent to finding the ‘density’ of inhabited types in the set of all types, or the so-called asymptotic probability of finding an inhabited type in the set of all types. Under the Curry–Howard isomorphism this means finding the density or asymptotic probability of provab

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31

LEUNG, FRANCIS KIT-NAM. "STATISTICAL INFERENCE FOR K INDEPENDENT, HOMOGENEOUS ARITHMETIC PROCESSES." International Journal of Reliability, Quality and Safety Engineering 07, no. 03 (2000): 223–36. http://dx.doi.org/10.1142/s0218539300000195.

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For k=1,…, K, a stochastic process {An,k, n =1, 2,…} is an arithmetic process (AP) if there exists some real number, d, so that {An,k +(n-1)d, n =1, 2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used to model a point process, i.e., point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for K independent, homogeneous APs.

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Lapko, A. V., and V. A. Lapko. "Estimation of traditional numerical characteristics of multimodal distribution laws of a one-dimensional random variable in conditions of large volume statistical data." Izmeritel`naya Tekhnika 74, no. 2 (2025): 47–54. https://doi.org/10.32446/0368-1025it.2025-2-47-54.

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The efficiency of estimating the traditional numerical characteristics of multimodal symmetric and asymmetric distribution laws of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, the formulas for discretization of the interval of values of a random variable by Sturgess, Brooks-Carruthers, Heinhold-Gaede and the formula for optimal discretization proposed by the authors of this article were used. For this purpose, data arrays have been formed that allow us to evaluate the numerical characteristics of the laws of

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33

KHAN, Nabiullah, Saddam HUSAİN, and Owais KHAN. "A novel kind of beta logarithmic function and their properties." Hacettepe Journal of Mathematics and Statistics 52, no. 4 (2023): 945–55. http://dx.doi.org/10.15672/hujms.1153572.

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The main objective is to introduce a novel kind of beta function known as the beta logarithmic function using extended beta functions and logarithmic mean. Further, we study its essential properties and investigate various formulas of beta logarithmic functions such as integral representation, summation formula, transform formula and their statistical properties. Based on this concept, we introduce new hypergeometric and confluent hypergeometric functions and study their properties.

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Barahmah, Salem Saleh. "A NEW EXTENSION OF LOGARITHMIC BETA FUNCTION AND THEIR PROPERTIES." Electronic Journal of University of Aden for Basic and Applied Sciences 5, no. 1 (2024): 123–30. http://dx.doi.org/10.47372/ejua-ba.2024.1.334.

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Khan Et Al., presented a new kind of beta logarithmic function, we aim in this research article to introduce new extension of beta logarithmic function, Further, we study its fundamental properties and discuss diverse formulas of that extension such as integral representation, summation formula, transform formula and their statistical properties. Based on this concept, we introduce new hypergeometric and confluent hypergeometric functions and study their properties.

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35

Salama, Ahmed A., Ahmed M. Hammad, and Khaled ElGhonemy S. Ahmed. "Evaluation of the accuracy of the Haigis-L, Barrett True-K formulas for calculating intraocular lens power in eyes that had previously undergone corneal refractive surgery." Journal of the Egyptian Ophthalmological Society 118, no. 3 (2025): 276–83. https://doi.org/10.4103/ejos.ejos_20_25.

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Aim This study aimed to evaluate and compare the accuracy of the Haigis-L, Barrett True-K formulas in predicting intraocular lens power for eyes that have undergone corneal refractive surgery. Patients and methods A retrospective study was conducted on 134 eyes with a history of corneal refractive surgery. The predictive accuracy of the Haigis-L and Barrett True-K formulas was analyzed and the prediction error for each formula was assessed. The postoperative refractive outcomes were compared to the target refraction to determine the more accurate formula. Statistical analysis used are statisti

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36

Palupi, Retno, Diyan Ayuk Yulianna, and SM Santi Winarsih. "Analisa Perbandingan Rumus Haversine Dan Rumus Euclidean Berbasis Sistem Informasi Geografis Menggunakan Metode Independent Sample t-Test." JITU : Journal Informatic Technology And Communication 5, no. 1 (2021): 40–47. http://dx.doi.org/10.36596/jitu.v5i1.494.

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Comparative Analysis of the Haversine Formula and the Euclidean Formula based on Geographical Information Systems which aims to analyze and compare the measurement results of the two formulas whether there are significant differences to the distance measured based on geographic information systems. Research objects used to collect distance data are several bank offices in the city of Solo. The method used in this research is to create a geographic information system application using web-based programming using the PHP (Pearl Hypertext Prepocessor) programming language, with the MySQL database

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Aristodemou, Petros, Nathaniel E. Knox Cartwright, John M. Sparrow, and Robert L. Johnston. "Statistical Analysis for Studies of Intraocular Lens Formula Accuracy." American Journal of Ophthalmology 160, no. 5 (2015): 1085–86. http://dx.doi.org/10.1016/j.ajo.2015.08.010.

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Lantuéjoul, Ch. "Some stereological and statistical consequences derived from Cartier's formula." Journal of Microscopy 151, no. 3 (1988): 265–76. http://dx.doi.org/10.1111/j.1365-2818.1988.tb04687.x.

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Syed Ahmad, Sharifah Sakinah, Siti Hajar Mohd Mushar, Nur Hajar Zamah Shari, and Fauziah Kasmin. "A Comparative study of log volume estimation by using statistical method." EDUCATUM Journal Of Science, Mathematics And Technology 7, no. 1 (2020): 22–28. http://dx.doi.org/10.37134/ejsmt.vol7.1.3.2020.

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Log volume estimation is a measurement of the amount of merchantable volume and precise estimation of log volume plays an important role in sustainable forest management. There are several log volume formula which commonly used in estimating the log volume, however, there are significant differences between each formula. Therefore, this paper evaluates the performance of three different log volume formula which are Smalian’s, Huber’s and Bruce’s formula against several log sectional length. The performance of each log volume formula will be evaluated in terms of the bias, precision and accurac

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Çınar, Muhammed, Dilan Şeker та Mikail Et. "(λ,μ) Statistical Convergence of Order γ for Double Sequences of Functions". ITM Web of Conferences 22 (2018): 01058. http://dx.doi.org/10.1051/itmconf/20182201058.

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In this present work, we investigate the concepts of Δr - statistical convergence of order [see formula in PDF] for double sequences of real valued functions. Also some definitions we given for Δr - statistical Cauchy sequence for double sequences of real valued functions and some relations between [see formula in PDF] statistical convergence and strong [see formula in PDF]-summability are given.

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Kumari, Sushma. "Finiteness of inverse moments of (m,n,β)-Laguerre matrices". Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, № 03 (2018): 1850022. http://dx.doi.org/10.1142/s0219025718500224.

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Wishart matrices are one of the fundamental matrix models in multivariate statistics. The classical Wishart ensemble has been generalized to [Formula: see text]-Laguerre ensemble for the values of [Formula: see text]. Many properties such as eigenvalue densities, moments and inverse moments of [Formula: see text]-Laguerre matrices are important in various fields of mathematics and physics. The moments and inverse moments of Wishart matrices have been studied rigorously and the explicit formulas were given in [P. Graczyk, G. Letac and H. Massam, Ann. Statist. 31 (2003) 287–309; S. Matsumoto, Ge

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Bracken, Joseph A. "God, Chance and Purpose: Implications for Process Theology." Process Studies 39, no. 1 (2010): 106–16. http://dx.doi.org/10.2307/44799095.

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Abstract In God, Chance and Purpose, David Bartholomew uses probability theory to show how Divine Providence can be active in a world governed by chance and necessity. At the micro-level of Nature God uses a statistical formula to control the outcome of seemingly random events; at the macro-level God influences but does not control the outcome of events. From a Whiteheadian perspective "the common element of form" of a society could be seen as the equivalent of Bartholomew’s statistical formula but generated in each case from the bottom-up rather than imposed from the top-down. Yet Bartholomew

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Huang, Man, Cia-chu Xia, Peng Sha, Cheng-rong Ma, and Shi-gui Du. "Correlation between the Joint Roughness Coefficient and Rock Joint Statistical Parameters at Different Sampling Intervals." Advances in Civil Engineering 2019 (July 29, 2019): 1–9. http://dx.doi.org/10.1155/2019/1643842.

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Joint roughness coefficient (JRC) is a major factor that affects the mechanical properties of rock joints. Statistical methods that are used to calculate the JRC increasingly depend on a sampling interval (Δx). The variation rules of fitting parameters a, b, and b/a at different Δx values were analyzed on the basis of the relationship between the JRC and statistical parameter Z2. The relationship between the fitting parameters a and b was deduced in accordance with the ten standard profiles proposed by Barton. Empirical formulas for the JRC, Z2, and Δx were also established. The estimation acc

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MOLITOR, MATHIEU. "REMARKS ON THE STATISTICAL ORIGIN OF THE GEOMETRICAL FORMULATION OF QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 09, no. 03 (2012): 1220001. http://dx.doi.org/10.1142/s0219887812200010.

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A quantum system can be entirely described by the Kähler structure of the projective space [Formula: see text] associated to the Hilbert space [Formula: see text] of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional quantum systems) and statistics through the natural geometry of the space [Formula: see text] of non-vanishing probabilities [Formula: see text] defined on a finite set En: = {x1, …, xn}. More precisely, we use the Fisher metric gF and the exponentia

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Angelelli, Mario, and Boris Konopelchenko. "Zeros and amoebas of partition functions." Reviews in Mathematical Physics 30, no. 09 (2018): 1850015. http://dx.doi.org/10.1142/s0129055x18500150.

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Singular sectors [Formula: see text] (loci of zeros) for real-valued non-positively defined partition functions [Formula: see text] of [Formula: see text] variables are studied. It is shown that [Formula: see text] have a stratified structure where each stratum is a set of certain hypersurfaces in [Formula: see text]. The concept of statistical amoeba is introduced and the properties of a family of statistical amoebas are studied. The relation with algebraic amoebas is discussed. Tropical limits of statistical amoebas are considered too. Applications of the concept of statistical amoeba to the

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Al-Solamy, Falleh R., Pooja Bansal, Bang-Yen Chen, Cengizhan Murathan, and Mohammad Hasan Shahid. "Geometry of Chen invariants in statistical warped product manifolds." International Journal of Geometric Methods in Modern Physics 17, no. 06 (2020): 2050081. http://dx.doi.org/10.1142/s0219887820500814.

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In this paper, we derive Chen inequality for statistical submanifold of statistical warped product manifolds [Formula: see text]. Further, we derive Chen inequality for Legendrian statistical submanifold in statistical warped product manifolds [Formula: see text]. We also provide some applications of derived inequalities in a statistical warped product manifold which is equivalent to a hyperbolic space. Moreover, we construct new examples of statistical warped product manifolds to support results.

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WANG, MINGJIN. "PROBABILISTIC DERIVATION OF A q-POLYNOMIALS TRANSFORMATION FORMULA." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 02 (2013): 1350017. http://dx.doi.org/10.1142/s0219025713500173.

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In this paper, we use the distribution W(x; q) and the Lebesgue's dominated convergence theorem to give a probabilistic derivation of a transformation formula for the Al-Salam-Carlitz polynomials. Some applications of the transformation are also given, which include an extension of the Heine's 2ϕ1 transformation formulas and an extension of the Bailey-Daum summation formula.

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Zhang, Yichi, Xiao Ying Liang, Shu Liu, Jacky W. Y. Lee, Srinivasan Bhaskar, and Dennis S. C. Lam. "Accuracy of Intraocular Lens Power Calculation Formulas for Highly Myopic Eyes." Journal of Ophthalmology 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/1917268.

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Purpose.To evaluate and compare the accuracy of different intraocular lens (IOL) power calculation formulas for eyes with an axial length (AL) greater than 26.00 mm.Methods.This study reviewed 407 eyes of 219 patients with AL longer than 26.0 mm. The refractive prediction errors of IOL power calculation formulas (SRK/T, Haigis, Holladay, Hoffer Q, and Barrett Universal II) using User Group for Laser Interference Biometry (ULIB) constants were evaluated and compared.Results.One hundred seventy-one eyes were enrolled. The Barrett Universal II formula had the lowest mean absolute error (MAE) and

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Patriota, Alexandre Galvão. "On Some Assumptions of the Null Hypothesis Statistical Testing." Educational and Psychological Measurement 77, no. 3 (2016): 507–28. http://dx.doi.org/10.1177/0013164416667979.

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Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis [Formula: see text] could be less supported by the data than a more restrictive hypothesis such as [Formula: see text], where [Formula: see text] and [Formula: see text] are two population means. This article intends to discuss and explicit some important assum

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Mil-Homens, João, Roshanka Ranasinghe, Jaap Van Thiel de Vries, and Marcel Stive. "RE-ASSESSMENT AND UPDATE OF BULK LONGSHORE SEDIMENT TRANSPORT FORMULAS." Coastal Engineering Proceedings 1, no. 33 (2012): 28. http://dx.doi.org/10.9753/icce.v33.sediment.28.

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Longshore sediment transport (LST) is one of the main drivers of beach morphology. Bulk LST formulas are routinely used in coastal management/engineering studies to assess LST rates and gradients. Over 50 years of research has resulted in several bulk LST formulas that have been tested with varying levels of rigor. In this study, the predictive skill of one of the most recent bulk LST formulas (Bayram et al., 2007) is evaluated. The calibration coefficients in the formula are improved using a least-squares optimization algorithm, resulting in a significant improvement in predictive skill. The

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