Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable

Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable

Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral <inline-formula><math display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-...

Full description

Bibliographic Details
Main Author:	Stefan M. Moser
Format:	Article
Language:	English
Published:	MDPI AG 2020-09-01
Series:	Entropy
Subjects:	central <i>χ</i><sup>2</sup> distribution chi-square distribution expected logarithm exponential distribution negative integer moments noncentral <i>χ</i><sup>2</sup> distribution
Online Access:	https://www.mdpi.com/1099-4300/22/9/1048

Similar Items

How to use χ2 test correctly——χ2 distribution and the related contents
by: Hu Chunyan, et al.
Published: (2021-02-01)

Heterotridentate Organomonophosphines in Pt(κ<sup>3</sup>–X<sup>1</sup>P<sup>1</sup>X<sup>2</sup>)(Y) (X<sup>1,2</sup> = N<sup>1,2</sup> or S<sup>1,2</sup>), Pt(κ<sup>3</sup>–P<sup>1</sup>N<sup>1</sup>X<sup>1</sup>)(Y) (X<sup>1</sup> = O, C, S or Se) Pt(κ<sup>3</sup>–P<sup>1</sup>S<sup>1</sup>Cl<sup>1</sup>)(Cl) and Pt(κ<sup>3</sup>–P<sup>1</sup>Si<sup>1</sup>N<sup>1</sup>)(OL)—Structural Aspects
by: Milan Melník, et al.
Published: (2022-12-01)

Embracing [XY<sub>3</sub>]<i><sup>m–</sup></i> and [XY<sub>4</sub>]<i><sup>m–</sup></i> Anions in Salts of [M(bpy)<sub>3</sub>]<i><sup>q</sup></i><sup>+</sup>
by: Edwin C. Constable, et al.
Published: (2023-01-01)

The Kauffman Bracket Skein Module of <i>S</i><sup>1</sup> × <i>S</i><sup>2</sup> via Braids
by: Ioannis Diamantis
Published: (2024-09-01)

Phototactic Changes in <i>Phthorimaea absoluta</i> Long-Wavelength Opsin Gene Mutants (<i>LW2<sup>−/−</sup></i>) and Short-Wavelength Opsin Gene Mutant (<i>BL<sup>−/−</sup></i>) Strains
by: Yanhong Tang, et al.
Published: (2024-06-01)

Structural Aspects of Pt(η<sup>3</sup>–P<sup>1</sup>C<sub>2</sub>X<sup>1</sup>C<sub>2</sub>P<sup>2</sup>)(Y) Derivative Types
by: Milan Melník, et al.
Published: (2023-09-01)

Measurement of Aβ Amyloid Plaques and Tau Protein in Postmortem Human Alzheimer’s Disease Brain by Autoradiography Using [<sup>18</sup>F]Flotaza, [<sup>125</sup>I]IBETA, [<sup>124/125</sup>I]IPPI and Immunohistochemistry Analysis Using QuPath
by: Rommani Mondal, et al.
Published: (2023-03-01)

<i>G</i><sup>2</sup> Hermite Interpolation by Segmented Spirals
by: Yuxuan Zhou, et al.
Published: (2022-12-01)

Spinach Plants Favor the Absorption of K<sup>+</sup> over Na<sup>+</sup> Regardless of Salinity, and May Benefit from Na<sup>+</sup> When K<sup>+</sup> is Deficient in the Soil
by: Jorge F. S. Ferreira, et al.
Published: (2020-04-01)

Ontogenetic Development of Gill and Na<sup>+</sup>/K<sup>+</sup> ATPase in the Air-Breathing Loach
by: Yaqiu Liu, et al.
Published: (2022-12-01)

Wound Repair and Ca<sup>2+</sup> Signalling Interplay: The Role of Ca<sup>2+</sup> Channels in Skin
by: Gregorio Bonsignore, et al.
Published: (2024-03-01)

A Thermal Sublimation Generator of <sup>131m</sup>Xe
by: Karolina Kulesz, et al.
Published: (2022-11-01)

The Effect of Decreased Ca<sup>++</sup>/Mg<sup>++</sup> ATPase Activity on <i>Lactobacillus delbrueckii</i> subsp. <i>bulgaricus</i> sp1.1 Survival during Spray Drying
by: Jialei Sun, et al.
Published: (2023-02-01)

Safranal Induces Vasorelaxation by Inhibiting Ca<sup>2+</sup> Influx and Na<sup>+</sup>/Ca<sup>2+</sup> Exchanger in Isolated Rat Aortic Rings
by: Noor Nadhim Al-Saigh, et al.
Published: (2022-06-01)

K<sup>+</sup> and Ca<sup>2+</sup> Channels Regulate Ca<sup>2+</sup> Signaling in Chondrocytes: An Illustrated Review
by: Yoshiaki Suzuki, et al.
Published: (2020-06-01)

Viewpoint Selection for 3D-Games with f-Divergences
by: Micaela Y. Martin, et al.
Published: (2024-05-01)

Mitochondrial DNA tRNA<sup>Leu</sup> and tRNA<sup>Ser</sup> polymorphism in different pig breeds
by: M. A. Kolosova, et al.
Published: (2018-10-01)

Effects of Sesamin, the Major Furofuran Lignan of Sesame Oil, on the Amplitude and Gating of Voltage-Gated Na<sup>+</sup> and K<sup>+</sup> Currents
by: Ping-Chung Kuo, et al.
Published: (2020-07-01)

A Functional K<sup>+</sup> Channel from Tetraselmis Virus 1, a Member of the <i>Mimiviridae</i>
by: Kerri Kukovetz, et al.
Published: (2020-09-01)

Transcription Factors Mcm1 and Sfp1 May Affect [<i>PSI</i><sup>+</sup>] Prion Phenotype by Altering the Expression of the <i>SUP35</i> Gene
by: Andrew G. Matveenko, et al.
Published: (2024-04-01)

Processing of Fluorescent Proteins May Prevent Detection of Prion Particles in [<i>PSI</i><sup>+</sup>] Cells
by: Andrew G. Matveenko, et al.
Published: (2022-11-01)

Phase I and II Clinical Trial Comparing the LBSap, Leishmune<sup>®</sup>, and Leish-Tec<sup>®</sup> Vaccines against Canine Visceral Leishmaniasis
by: Rodrigo Dian de Oliveira Aguiar-Soares, et al.
Published: (2020-11-01)

Targeting PirA<i><sup>vp</sup></i> and PirB<i><sup>vp</sup></i> Toxins of <i>Vibrio parahaemolyticus</i> with Oilseed Peptides: An In Silico Approach
by: Joe-Hui Ong, et al.
Published: (2021-10-01)

How to use χ2 test correctly——the Wald΄s test and the implementation of SAS software
by: Hu Chunyan, et al.
Published: (2021-12-01)

Immobilization of Cellulolytic Enzymes in Accurel<sup>®</sup> MP1000
by: Julia R. S. Baruque, et al.
Published: (2023-06-01)

Fixed Point Results in <i>C</i><sup>🟉</sup>-Algebra-Valued Partial <i>b</i>-Metric Spaces with Related Application
by: Gunaseelan Mani, et al.
Published: (2023-02-01)

Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables
by: Peter M. B. Cahusac
Published: (2024-04-01)

NH<sub>4</sub><sup>+</sup> Toxicity, Which Is Mainly Determined by the High NH<sub>4</sub><sup>+</sup>/K<sup>+</sup> Ratio, Is Alleviated by CIPK23 in <i>Arabidopsis</i>
by: Sujuan Shi, et al.
Published: (2020-04-01)

Na<sup>+</sup>,K<sup>+</sup>-ATPase with Disrupted Na<sup>+</sup> Binding Sites I and III Binds Na<sup>+</sup> with Increased Affinity at Site II and Undergoes Na<sup>+</sup>-Activated Phosphorylation with ATP
by: Hang N. Nielsen, et al.
Published: (2024-01-01)

A Dinitrophenol-Based Colorimetric Chemosensor for Sequential Cu<sup>2+</sup> and S<sup>2−</sup> Detection
by: Hyejin Nam, et al.
Published: (2023-02-01)

Physiological and Pathophysiological Roles of Mitochondrial Na<sup>+</sup>-Ca<sup>2+</sup> Exchanger, NCLX, in Hearts
by: Ayako Takeuchi, et al.
Published: (2021-12-01)

Organomonophosphines in Pt(η<sup>3</sup>-X<sup>1</sup>X<sup>2</sup>X<sup>3</sup>)(PR<sub>3</sub>), (X = N<sup>1</sup>, N<sup>2</sup>, N<sup>3</sup>; S<sup>1</sup>, S<sup>2</sup>, S<sup>3</sup>; or Te<sup>1</sup>, Te<sup>2</sup>, Te<sup>3</sup>) Derivatives: Structural Aspects
by: Milan Melník, et al.
Published: (2023-06-01)

β<sup>2</sup>-<i>Homo</i>-Amino Acid Scan of µ-Selective Opioid Tetrapeptide TAPP
by: Dagmara Tymecka, et al.
Published: (2020-05-01)

Percentile Study of χ Distribution. Application to Response Time Data
by: Juan Carlos Castro-Palacio, et al.
Published: (2020-04-01)

Solving Inverse Problem of Distributed-Order Time-Fractional Diffusion Equations Using Boundary Observations and <i>L</i><sup>2</sup> Regularization
by: Lele Yuan, et al.
Published: (2023-07-01)

Depletion of Na<sup>+</sup>/H<sup>+</sup> Exchanger Isoform 1 Increases the Host Cell Resistance to <i>Trypanosoma cruzi</i> Invasion
by: João Paulo Ferreira Rodrigues, et al.
Published: (2022-11-01)

A Versatile Broadband Attached Proton Test Experiment for Routine <sup>13</sup>C Nuclear Magnetic Resonance Spectroscopy
by: Peter Bigler, et al.
Published: (2024-02-01)

Computation of cumulative density of noncentral chi-square distribution in Excel
by: Sambaraju, Prasanth
Published: (2022-10-01)

Effect of Mn<sup>2+</sup>/Zn<sup>2+</sup>/Fe<sup>3+</sup> Oxy(Hydroxide) Nanoparticles Doping onto Mg-Al-LDH on the Phosphate Removal Capacity from Simulated Wastewater
by: Diana Guaya, et al.
Published: (2022-10-01)

Radioiodinated Tau Imaging Agent III Molecular Modeling, Synthesis, and Evaluation of a New Tau Imaging Agent, [<sup>125</sup>I]ISAS in Post-Mortem Human Alzheimer’s Disease Brain
by: Stephanie A. Sison, et al.
Published: (2024-07-01)