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Journal articles on the topic 'K-statistics'

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Published: 7 July 2024

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1

Fu, Shishuo, Guo-Niu Han, and Zhicong Lin. "$k$-Arrangements, Statistics, and Patterns." SIAM Journal on Discrete Mathematics 34, no. 3 (January 2020): 1830–53. http://dx.doi.org/10.1137/20m1340538.

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2

Di Nardo, E., and D. Senato. "A symbolic method for k-statistics." Applied Mathematics Letters 19, no. 9 (September 2006): 968–75. http://dx.doi.org/10.1016/j.aml.2005.09.012.

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3

Warrens, Matthijs J. "Inequalities Between Kappa and Kappa-Like Statistics for k×k Tables." Psychometrika 75, no. 1 (September 23, 2009): 176–85. http://dx.doi.org/10.1007/s11336-009-9138-8.

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4

Yamamoto, Keiji, Atsuya Uno, Hitoshi Murai, Toshiyuki Tsukamoto, Fumiyoshi Shoji, Shuji Matsui, Ryuichi Sekizawa, et al. "The K computer Operations: Experiences and Statistics." Procedia Computer Science 29 (2014): 576–85. http://dx.doi.org/10.1016/j.procs.2014.05.052.

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5

Boos, Dennis D. "Comparing K Populations with Linear Rank Statistics." Journal of the American Statistical Association 81, no. 396 (December 1986): 1018. http://dx.doi.org/10.2307/2289077.

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6

McCullagh, Peter, and Daryl Pregibon. "$k$-Statistics and Dispersion Effects in Regression." Annals of Statistics 15, no. 1 (March 1987): 202–19. http://dx.doi.org/10.1214/aos/1176350261.

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7

Dutt, Vinayak, and James F. Greenleaf. "Ultrasound Echo Envelope Analysis Using a Homodyned K Distribution Signal Model." Ultrasonic Imaging 16, no. 4 (October 1994): 265–87. http://dx.doi.org/10.1177/016173469401600404.

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The statistics of ultrasound echo envelope signals can be used to characterize scattering media. The Rayleigh distribution and its generalized forms, the K and Rice distributions, have been previously used to model the echo signal. A more generalized statistical model, the homodyned K distribution, combines the K and Rice distribution features to better account for the statistics of the echo signal. We show that this model can give two parameters that are useful for media characterization: k, the ratio of coherent to diffuse signals, and, β, which characterizes the clustering of scatterers in the medium.

8

Speed, T. P. "Cumulants and partition lattices II: generalised k-statistics." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 34–53. http://dx.doi.org/10.1017/s1446788700026483.

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AbstractThe role played by the Möbius function of the lattice of all partitions of a set in the theory of k-statistics and their generalisations is pointer out and the main results conscerning these statistics are drived. The definitions and formulae for the expansion of products of generalished k-statistics are presented from this viewpoint and applied to arrays of random variables whos moments satisfy stitable symmentry constraints. Applications of the theory are given including the calculation of (joint) cumulants of k-statistics, the minimum variace estimation of (generalised) moments and the asymptotic behaviour of generalised k-statistics viewed as (reversed) martingales.

9

Kislitsyn, Alexey Alexeevich, and Yurii Nikolaevich Orlov. "The investigation of the k-NN graph statistics." Keldysh Institute Preprints, no. 85 (2021): 1–23. http://dx.doi.org/10.20948/prepr-2021-85.

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In this paper the investigation of the structure of k-NN graph is presented. The purpose of this analysis is to match the probability of implementation particular graph under assumption of a certain distribution of distances between vertices and depending on the number of vertices. Sample distributions of the graph by the number of disconnected fragments, fragments by the number of vertices, and vertices by the degrees of incoming edges are used as the main statistics. As an example, the problem of identifying the author of a text by the n-gram method is considered.

10

Yao, Suxia, Yu Miao, and Saralees Nadarajah. "Exponential convergence for the k-th order statistics." Filomat 29, no. 5 (2015): 977–84. http://dx.doi.org/10.2298/fil1505977y.

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Let X1,X2,...,Xn be the samples of an arbitrary population having a uniform distribution on the interval [0,1] and X1,n ? X2,n ?...? Xn,n denote the order statistics. The moderate deviations, large deviations and Cram?r large deviations for the k-th order statistics Xk,n are established. Furthermore, we also discuss the case that the samples come from the general distribution F.

11

Remmel, J. B. "Permutation statistics and (k,l)-hook Schur functions." Discrete Mathematics 67, no. 3 (December 1987): 271–98. http://dx.doi.org/10.1016/0012-365x(87)90178-6.

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12

Lin, Yujing, Barry L. Nelson, and Linda Pei. "Virtual Statistics in Simulation via k Nearest Neighbors." INFORMS Journal on Computing 31, no. 3 (July 2019): 576–92. http://dx.doi.org/10.1287/ijoc.2018.0839.

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13

Kokot, Marek, Maciej Długosz, and Sebastian Deorowicz. "KMC 3: counting and manipulating k-mer statistics." Bioinformatics 33, no. 17 (May 4, 2017): 2759–61. http://dx.doi.org/10.1093/bioinformatics/btx304.

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14

Liu, Shao-Hua. "Statistics on trapezoidal words and k-inversion sequences." Discrete Applied Mathematics 325 (January 2023): 1–8. http://dx.doi.org/10.1016/j.dam.2022.10.010.

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15

Irving, John, and Amarpreet Rattan. "k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests." Advances in Applied Mathematics 151 (October 2023): 102566. http://dx.doi.org/10.1016/j.aam.2023.102566.

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16

Muraleedharan, Laji, and Manoj Chacko. "Interval prediction of order statistics and record values using concomitants of order statistics and record values for Morgenstern family of distributions." Journal of Statistical Research 56, no. 1 (February 1, 2023): 55–73. http://dx.doi.org/10.3329/jsr.v56i1.63946.

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In this paper, we discuss the problem of predicting intervals for future order statistics and k-record values based on observed concomitants of order statistics and observed concomitants of k-record values arising from a Morgenstern family of distributions. The coverage probabilities obtained are accurate and independent of the parent distribution. A real data set is also considered to exemplify the proposed methodologies developed in this paper. Journal of Statistical Research 2022, Vol. 56, No. 1, pp. 55-72

17

Burkschat, M., and J. Navarro. "AGING PROPERTIES OF SEQUENTIAL ORDER STATISTICS." Probability in the Engineering and Informational Sciences 25, no. 4 (July 21, 2011): 449–67. http://dx.doi.org/10.1017/s026996481100012x.

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Sequential order statistics describe the ordered failure times in a k-out-of-n system, where the failures of components might affect the performance of remaining working components. In this article aging properties of sequential order statistics are examined and conditions are given such that the distribution of a sequential order statistic is ILR, IFR, IFRA, or NBU. Moreover, conditions for aging properties of spacings of sequential order statistics are obtained.

18

Moon, Hyoung-Jin, Jong-ho Nam, and Katarzyna Juszczyk-Frelkiewicz. "Awareness of K-Culture Among Polish University Students and Preferred Teaching Methods." New Educational Review 73, no. 3 (2023): 95–108. http://dx.doi.org/10.15804/tner.23.73.3.07.

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This study explores the most preferred and effective teaching methods for Korean language and culture for university students. Statistical analysis of awareness of the Korean language, history, and culture was conducted. It tested differences in students’ knowledge about Korea dependently on a teaching method and sociodemographic variables. The study investigated is there a dependency between favourite teaching methods of K-culture and analogical methods using K-pop, K-drama, and K-food. The main research tool was the survey conducted among 70 students studying Korean language and culture at the University of Silesia in Katowice, Poland. The study’s statistical analyses employed the IBM SPSS Statistics 29.0 package, used for analysing basic descriptive statistics, r Pearson and rho Spearman correlation analyses, and t Student test for independent variables. The analysis proves that the students do not differ in terms of knowledge about Korea in relation to a preferred and effective teaching method.

19

Shiraishi, Taka-aki. "ON SCALE-INVARIANT M-STATISTICS IN MULTIVARIATE K SAMPLES." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 26, no. 2 (1996): 241–53. http://dx.doi.org/10.14490/jjss1995.26.241.

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20

Lustmann, Yochay, and Dana Porrat. "Indoor Channel Spectral Statistics, K-Factor and Reverberation Distance." IEEE Transactions on Antennas and Propagation 58, no. 11 (November 2010): 3685–92. http://dx.doi.org/10.1109/tap.2010.2071354.

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21

Yushchenko, O. P., S. A. Akimenko, K. S. Belous, G. I. Britvich, I. G. Britvich, K. V. Datsko, A. P. Filin, et al. "High statistics study of the K−→π0μ−ν decay." Physics Letters B 581, no. 1-2 (February 2004): 31–38. http://dx.doi.org/10.1016/j.physletb.2003.12.002.

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22

Speed, T. P., and H. L. Silcock. "Cumulants and Partition Lattices V. Calculating Generalized k-Statistics." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 2 (April 1988): 171–96. http://dx.doi.org/10.1017/s1446788700029773.

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AbstractA method is developed for obtaining compact, easily computed and statistically interpretable expressions for the generalized k-statistics associated with multiply-indexed arrays of random variables such as those which arise in variance component analysis. These expressions will be used in the next paper in this series to give formulae for variances and covariances of estimates of components of variance.

23

Raqab, Mohammad Z., and Wael A. Amin. "A note on reliability properties of k-record statistics." Metrika 46, no. 1 (January 1997): 245–51. http://dx.doi.org/10.1007/bf02717177.

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24

Martínez-Camblor, Pablo, Carlos Carleos, and Norberto Corral. "Powerful nonparametric statistics to compare k independent ROC curves." Journal of Applied Statistics 38, no. 7 (March 30, 2011): 1317–32. http://dx.doi.org/10.1080/02664763.2010.498504.

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25

Deheuvels, Paul. "Strong laws for the k-th order statistic when k?c log2 n." Probability Theory and Related Fields 72, no. 1 (April 1986): 133–54. http://dx.doi.org/10.1007/bf00343900.

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26

Bedbur, Stefan, and Udo Kamps. "Testing for Equality of Parameters from Different Load-Sharing Systems." Stats 2, no. 1 (January 29, 2019): 70–88. http://dx.doi.org/10.3390/stats2010006.

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In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k-out-of-n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures.

27

Randriamaro, Hery. "A Deformed Quon Algebra." Communications in Mathematics 27, no. 2 (December 1, 2019): 103–12. http://dx.doi.org/10.2478/cm-2019-0010.

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AbstractThe quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators ai,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations {a_j}_{,l}a_{i,k}^\dagger = qa_{i,k}^\dagger{a_{j,l}} + {q^{{\beta _{k,l}}}}{\delta _{i,j}} We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of ai,k’s and a_{i,k}^\dagger ‘s to a vacuum state |0〉 is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.

28

Luczak, Brian B., Benjamin T. James, and Hani Z. Girgis. "A survey and evaluations of histogram-based statistics in alignment-free sequence comparison." Briefings in Bioinformatics 20, no. 4 (December 6, 2017): 1222–37. http://dx.doi.org/10.1093/bib/bbx161.

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Abstract Motivation Since the dawn of the bioinformatics field, sequence alignment scores have been the main method for comparing sequences. However, alignment algorithms are quadratic, requiring long execution time. As alternatives, scientists have developed tens of alignment-free statistics for measuring the similarity between two sequences. Results We surveyed tens of alignment-free k-mer statistics. Additionally, we evaluated 33 statistics and multiplicative combinations between the statistics and/or their squares. These statistics are calculated on two k-mer histograms representing two sequences. Our evaluations using global alignment scores revealed that the majority of the statistics are sensitive and capable of finding similar sequences to a query sequence. Therefore, any of these statistics can filter out dissimilar sequences quickly. Further, we observed that multiplicative combinations of the statistics are highly correlated with the identity score. Furthermore, combinations involving sequence length difference or Earth Mover’s distance, which takes the length difference into account, are always among the highest correlated paired statistics with identity scores. Similarly, paired statistics including length difference or Earth Mover’s distance are among the best performers in finding the K-closest sequences. Interestingly, similar performance can be obtained using histograms of shorter words, resulting in reducing the memory requirement and increasing the speed remarkably. Moreover, we found that simple single statistics are sufficient for processing next-generation sequencing reads and for applications relying on local alignment. Finally, we measured the time requirement of each statistic. The survey and the evaluations will help scientists with identifying efficient alternatives to the costly alignment algorithm, saving thousands of computational hours. Availability The source code of the benchmarking tool is available as Supplementary Materials.

29

Boutsikas, M. V., M. V. Koutras, and F. S. Milienos. "Asymptotic results for the multiple scan statistic." Journal of Applied Probability 54, no. 1 (March 2017): 320–30. http://dx.doi.org/10.1017/jpr.2016.102.

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AbstractThe contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at least r successes among them (r≤k≤n). In this paper we establish some asymptotic results for the distribution of the multiple scan statistic, as n,k,r→∞ and illustrate their accuracy through a simulation study. Our approach is based on an appropriate combination of compound Poisson approximation and random walk theory.

30

Basiri, Elham, and Jafar Ahmadi. "Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records." Computational Statistics 28, no. 6 (July 14, 2013): 2825–48. http://dx.doi.org/10.1007/s00180-013-0430-9.

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31

Sulewski, Piotr. "Modyfikacja testu niezależności." Wiadomości Statystyczne. The Polish Statistician 2013, no. 10 (October 28, 2013): 1–19. http://dx.doi.org/10.59139/ws.2013.10.1.

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This paper proposes a modification of the classic test of independence chi-square involving the use of modular statistics, as a measure of discrepancy between the observed and hypothetical distribution. Module statistics differs from Pearson chi-square statistics that deviation square of the theoretical and expected empirical probability is replaced by absolute value. For the proposed statistics is given the critical value |Χ|α α by different size samples of significance α∈{0,01; 0,05; 0,1}. The ability of two-part tables was examined to detect a relationship between characteristics, defined as the power of the test as well as the results were compared with the power of the test of independence, using statistics by Χ2 z (k-1)(w-1) degrees of freedom. The author examined whether the distribution of discrepancy measurements of two-part tables is consistent with the theoretical distribution of chi-square by Χ2 z (k-1)(w-1) degrees of freedom. Their usefulness in statistical practice was indicated too.

32

Viertl, R. "G. K. Kanji (2006): 100 Statistical Tests." Statistical Papers 50, no. 3 (June 10, 2008): 683. http://dx.doi.org/10.1007/s00362-008-0145-0.

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33

Friel, Susan N., and Rebecca B. Corwin. "Implementing the Standards: The Statistics Standards in K–8 Mathematics." Arithmetic Teacher 38, no. 2 (October 1990): 35–39. http://dx.doi.org/10.5951/at.38.2.0035.

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34

Goel, Ritu, H. C. Taneja, and Vikas Kumar. "Measure of entropy for past lifetime and k-record statistics." Physica A: Statistical Mechanics and its Applications 503 (August 2018): 623–31. http://dx.doi.org/10.1016/j.physa.2018.02.200.

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35

Zhou, Nian Hong. "Eventual log-concavity of k-rank statistics for integer partitions." Journal of Number Theory 259 (June 2024): 242–72. http://dx.doi.org/10.1016/j.jnt.2024.01.003.

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36

Mirza, Babur M. "N-soliton statistics and condensate formation in dense quantum gases." Modern Physics Letters B 28, no. 25 (September 24, 2014): 1450200. http://dx.doi.org/10.1142/s0217984914502005.

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Statistics of N quantum density soliton waves [B. M. Mirza, Mod. Phys. Lett. B28 (2014) 1450148] is extended here to the case of systems with symmetric wave function. Since many such systems exhibit condensation phenomena, application is made of the soliton wave statistics to investigate condensation and phase transition in quantum gases such as 4 He and also dense systems such as the alkali atoms. Specific heat discontinuities are used to determine the condensation temperature for dense quantum gases and liquids. For the model case of helium the statistical theory is shown to predict not only the observed superfluid condensation temperature (2.17 ± 0.01 K) correctly but also the normal condensation temperature (4.21 ± 0.02 K), as well as the exact specific heat λ-profile.

37

Mirfarah, Elham, and Jafar Ahmadi. "Pitman closeness of $$k$$ k -records from two sequences to progressive Type-II censored order statistics." Computational Statistics 29, no. 5 (April 6, 2014): 1279–300. http://dx.doi.org/10.1007/s00180-014-0491-4.

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38

Sibagatullin, S. K., A. S. Kharchenko, and L. D. Devyatchenko. "Evaluation of uneven distribution of charge materials at blast furnace." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 61, no. 10 (November 14, 2018): 766–73. http://dx.doi.org/10.17073/0368-0797-2018-10-766-773.

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In various industries, the uneven distribution of material and energy resources significantly affects stability of the technological process and reduces the quality of products. In particular, in the blastfurnace production, the uneven distribution of charge materials and the temperature of gases significantly affect technical and economic performance of the furnace. The analysis of bibliographic sources has shown that for the estimation of unevenness various coefficients were generally used, taking into account the variability of material and ener gy resources in the production process, the coefficient of variation introduced by K. Pierson in 1895 was the most widespread. It was determined the relation between the square of the coefficient of variation of V2 and the value X2= (n(N-1))/N*V2according to which the random variable V2 has X2k a distribution with k degrees of freedom, k = N – 1, where n = n1 + n2 + … + nN, ni is the value of the i-th measurement, i = 1, N – is the number of measurements. The proposed method for estimating the unevenness is based on statistics X2k, and X2also introduced by K. Pearson in 1901 and 1904, respectively. The latter was intended to test the H0-correspondence of the empirical and statistical distribution. The method for determining the circumferential irregularity in the distribution of materials and gases in a blast furnace is based on the consistency of X2k and X2 of Pearson statistics, using the so-called quantile factor q, if in calculations of X2 the valu es of the ,physical quantities themselves are used, by analogy, not the frequency of the measured quantities. In this method, X2-statistic after correction was used to determine the measure of deviation (p) from the uniform distribution, i.e. the unevenness coefficientp = p(X2/k), p є (0; 1 – α), X2k = X2max= qX2 was calculated. In order to reconcile X2 and X2k statistics with the measurements of the physical quantities (temperature, pressure) or materials (granular, gaseous), the X2-statistic must be adjusted so that qX2max≈ X2k(α), X2max с(X21,..., Х2M )where M – is the number of experiments for which the values of X2-statics were determined, X2k(α) – the upper α-quantile of X2k statistic, q – the quantile multiplier, introduced for the correction of the X2-statistic values, X2max– the maximum value of X2-statistic is admissible for determining the measure of non-uniformity.The method was tested to evaluate the relative non-uniformity of the loaded charge components and the distribution of peripheral temperature at blast furnaces of OJSC “MMK” with volume of 2014 and 1370 m3. The influence of the sequence of a set of charge components in the hopper of a bell-less charging device of the furnace on the coefficient of circumferential unevenness (p) and the technical and economic parameters of melting was revealed.

39

Biau, Gérard, Benoît Cadre, and Laurent Rouvière. "Statistical analysis of k-nearest neighbor collaborative recommendation." Annals of Statistics 38, no. 3 (June 2010): 1568–92. http://dx.doi.org/10.1214/09-aos759.

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40

Rotondi, Renata. "Tests of Randomness Based on the K-NN Distances for Data from a Bounded Region." Probability in the Engineering and Informational Sciences 7, no. 4 (October 1993): 557–69. http://dx.doi.org/10.1017/s0269964800003132.

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This paper proposes some new statistics based on k-NN distances for assessing the uniformity of a set of points belonging to a d-dimensional bounded region. Size and power of the tests have been estimated and compared to those of the modified Hopkins' statistic.

41

Pérez, T., and J. A. Pardo. "The K ϕ-Divergence Statistic for Categorical Data Problems." Metrika 63, no. 3 (January 10, 2006): 355–69. http://dx.doi.org/10.1007/s00184-005-0025-8.

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42

Andrzejczak, Karol. "Application of the order statistics to the fault tolerant systems / Zastosowanie statystyk porządkowych do systemów tolerujących uszkodzenia." Journal of KONBiN 38, no. 1 (October 1, 2016): 77–98. http://dx.doi.org/10.1515/jok-2016-0019.

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Abstract Various models of ordered random variables having different interpretations have been introduced and studied extensively in the literature. The most popular of these are order statistics obtained by arranging n random variables (rv’s) in non-decreasing order of magnitude. Order statistics appear in many areas of statistical theory and applications including quality control, robustness, outlier detection, and reliability analysis. In this paper we study the construction of the functional and numerical reliability characteristics for the fault tolerant systems with so called “k-out-of-n” threshold reliability structure based on order statistics.

43

Huang, Guan-Da, Xue-Mei Liu, Tian-Lai Huang, and Li C. Xia. "The statistical power of k-mer based aggregative statistics for alignment-free detection of horizontal gene transfer." Synthetic and Systems Biotechnology 4, no. 3 (September 2019): 150–56. http://dx.doi.org/10.1016/j.synbio.2019.08.001.

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44

Kaesmetan, Yampi R. "PERBANDINGAN EKSTRAKSI TEKSTUR CITRA UNTUK PEMILIHAN BENIH KEDELAI DENGAN METODE STATISTIK ORDE I DAN STATISTIK ORDE II." High Education of Organization Archive Quality: Jurnal Teknologi Informasi 10, no. 2 (December 31, 2018): 92–102. http://dx.doi.org/10.52972/hoaq.vol10no2.p92-102.

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The problem in determining the selection of soybean seeds for replanting, especially in East Nusa Tenggara is still an important issue. The thing that affects the quality of soybean seeds is found broken seeds, dull seeds, dirty seeds, and broken seeds due to the process of drying and shelling. Determination of soy bean quality is usually done manually by visual observation. The manual system takes a long time and produces products with inconsistent quality due to visual limitations, fatigue, and different perceptions of each observer. This research was conducted using comparison of image texture extraction with statistical methods of order I (color moment) and order II statistics (GLCM) for soy bean selection. Order I statistics (color moment) show the probability of the appearance of the value of the gray degree of pixels in an image, while the order II statistics (GLCM) show the probability of a neighborhood relationship between two pixels that form a cohesion matrix from the image data. This research is expected to help the classification process in determining soybean seeds. The k-Nearest Neighbor (k-NN) algorithm used in previous studies to classify the image objects to be examined. The results of this study were successfully conducted using k-Nearest Neighbor (k-NN) with euclidean distance and k = 1 with the results of color moment extracts getting the highest accuracy of 88% and the results of GLCM feature extraction for homogeneity characteristics of 75.5%, correlations of 78.67% , contrast is 65.75% and energy is 63.83% with an average accuracy of 70.93%.

45

Kwasny, Mary J. "Statistics in K–12: Educators, Students, and Us: Challenges and resources for K–12 educators and students." CHANCE 28, no. 4 (October 2, 2015): 26–29. http://dx.doi.org/10.1080/09332480.2015.1120124.

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46

Di Nardo, Elvira, Giuseppe Guarino, and Domenico Senato. "A unifying framework for $k$-statistics, polykays and their multivariate generalizations." Bernoulli 14, no. 2 (May 2008): 440–68. http://dx.doi.org/10.3150/07-bej6163.

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47

Sarper, Huseyin, Roger W. Johnson, and Phermsak Siriphala. "Greatest Critical Difference Statistics in k-out-of-n Reliability Structures." Journal of Spacecraft and Rockets 35, no. 2 (March 1998): 232–35. http://dx.doi.org/10.2514/2.3316.

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48

Dimri, A. P., and U. C. Mohanty. "Snowfall Statistics of Some SASE Field Stations in J&K." Defence Science Journal 49, no. 5 (January 1, 1999): 437–45. http://dx.doi.org/10.14429/dsj.49.3858.

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49

Obraztsov, V. "High statistics measurement of the K+→π0e+ν(Ke3) decay formfactors." Nuclear and Particle Physics Proceedings 273-275 (April 2016): 1330–33. http://dx.doi.org/10.1016/j.nuclphysbps.2015.09.213.

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50

Speed, T. P. "Cumulants and partition lattices IV: a.s. convergence of generalised k-statistics." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 1 (August 1986): 79–94. http://dx.doi.org/10.1017/s1446788700028093.

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Abstract:

AbstractGeneralised k-statistics associated with multi-indexed arrays of random variables satisfying a generalised form of exchangeability are studied. By showing that they form multi-indexed reversed martingales and that the associated family of σ-fields possesses certain conditional independence properties, conditions for the a.s. convergence of generalised k-statistics are obtained. When the arrays of random variables are sums of independent arrays of independent effects, as is the case with the standard random effects anova models, the limits are identified as the associated generalixed cumulants.