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Journal articles on the topic 'Recursive moments'

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Published: 10 December 2022
Last updated: 29 January 2023

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1

Chong, Chee-Way, P. Raveendran, and R. Mukundan. "An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 06 (September 2003): 1011–23. http://dx.doi.org/10.1142/s0218001403002769.

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Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.
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2

Rincón, Luis. "A moment recursive formula for a class of distributions." Revista de Matemática: Teoría y Aplicaciones 28, no. 2 (July 6, 2021): 261–77. http://dx.doi.org/10.15517/rmta.v28i2.44507.

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We provide a recursive formula for the computation of moments of distributions belonging to a subclass of the exponential family. This subclass includes important cases as the binomial, negative binomial, Poisson, gamma and normal distribution, among others. The recursive formula provides a procedure to sequentially calculate the moments using only elementary operations. The approach makes no use of the moment generating function.
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3

KIM, JI HYUN. "CODES ASSOCIATED WITH Sp(4,q) AND EVEN-POWER MOMENTS OF KLOOSTERMAN SUMS." Bulletin of the Australian Mathematical Society 79, no. 3 (April 17, 2009): 427–35. http://dx.doi.org/10.1017/s0004972708001366.

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AbstractHere we derive a recursive formula for even-power moments of Kloosterman sums or equivalently for power moments of two-dimensional Kloosterman sums. This is done by using the Pless power-moment identity and an explicit expression of the Gauss sum for Sp(4,q).
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4

Kuba, Markus, and Alois Panholzer. "Limiting Distributions for a Class Of Diminishing Urn Models." Advances in Applied Probability 44, no. 1 (March 2012): 87–116. http://dx.doi.org/10.1239/aap/1331216646.

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In this work we analyze a class of 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix and c = pa with . We determine limiting distributions by obtaining a precise recursive description of the moments of the considered random variables, which allows us to deduce asymptotic expansions of the moments. In particular, we obtain limiting distributions for the pills problem a = c = d = 1, originally proposed by Knuth and McCarthy. Furthermore, we also obtain limiting distributions for the well-known sampling without replacement urn, a = d = 1 and c = 0, and generalizations of it to arbitrary and c = 0. Moreover, we obtain a recursive description of the moment sequence for a generalized problem.
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5

Kuba, Markus, and Alois Panholzer. "Limiting Distributions for a Class Of Diminishing Urn Models." Advances in Applied Probability 44, no. 01 (March 2012): 87–116. http://dx.doi.org/10.1017/s0001867800005462.

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In this work we analyze a class of 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix and c = pa with . We determine limiting distributions by obtaining a precise recursive description of the moments of the considered random variables, which allows us to deduce asymptotic expansions of the moments. In particular, we obtain limiting distributions for the pills problem a = c = d = 1, originally proposed by Knuth and McCarthy. Furthermore, we also obtain limiting distributions for the well-known sampling without replacement urn, a = d = 1 and c = 0, and generalizations of it to arbitrary and c = 0. Moreover, we obtain a recursive description of the moment sequence for a generalized problem.
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6

Hesselager, Ole. "A Recursive Procedure for Calculation of some Compound Distributions." ASTIN Bulletin 24, no. 1 (May 1994): 19–32. http://dx.doi.org/10.2143/ast.24.1.2005078.

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AbstractWe consider compound distributions where the counting distribution has the property that the ratio between successive probabilities may be written as the ratio of two polynomials. We derive a recursive algorithm for the compound distribution, which is more efficient than the one suggested by Panjer & Willmot (1982) and Willmot & Panjer (1987). We also derive a recursive algorithm for the moments of the compound distribution. Finally, we present an application of the recursion to the problem of calculating the probability of ruin in a particular mixed Poisson process.
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7

HOSNY, KHALID M. "EFFICIENT COMPUTATION OF LEGENDRE MOMENTS FOR GRAY LEVEL IMAGES." International Journal of Image and Graphics 07, no. 04 (October 2007): 735–47. http://dx.doi.org/10.1142/s021946780700288x.

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Direct computation of Legendre orthogonal moments requires huge arithmetic operations, which is very time consuming. Many works have described methods for reducing the computations involved in evaluating Legendre moments. Nevertheless, reduction computational complexity is still an open problem and needs more investigation. Existing algorithms mainly focused on binary images and compute Legendre moments using a set of geometric moments. We propose a fast and efficient method for computation of Legendre moments for binary and gray level images. A recurrence formula of one-dimensional Legendre moments will be established using the recursive property of Legendre polynomials; then the method will be extended to calculate the two-dimensional Legendre moments. This method is completely independent on geometric moment. The complexity analysis shows that the proposed method computes Legendre moments more efficiently than the direct method and the other conventional methods.
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8

Dräger, Lena. "RECURSIVE INATTENTIVENESS WITH HETEROGENEOUS EXPECTATIONS." Macroeconomic Dynamics 20, no. 4 (October 9, 2015): 1073–100. http://dx.doi.org/10.1017/s1365100514000741.

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We model agents' endogenous updating of information sets over time under changing macroeconomic conditions. Building on sticky information models, the degree of inattentiveness is endogenized by allowing agents to choose between a costly full-information predictor and a costless sticky-information predictor. This is modeled as a choice between discrete alternatives under rational inattention. Recursive simulation shows that the dynamic equilibrium paths of aggregate variables are highly persistent and match the moments of U.S. data better than a model with fixed sticky information or with sticky prices, especially with regard to higher moments and the degree of persistence. Predictors are chosen in line with the predictions from rational inattention models, as the aggregate degree of attentiveness increases with rising variance of the forecast variable. Moreover, the model can generate hump-shaped impulse responses of inflation to a monetary policy shock if the degree of inattentiveness is sufficiently high.
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9

Hillier, Grant, Raymond Kan, and Xiaolu Wang. "GENERATING FUNCTIONS AND SHORT RECURSIONS, WITH APPLICATIONS TO THE MOMENTS OF QUADRATIC FORMS IN NONCENTRAL NORMAL VECTORS." Econometric Theory 30, no. 2 (October 17, 2013): 436–73. http://dx.doi.org/10.1017/s0266466613000364.

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Recursive relations for objects of statistical interest have long been important for computation, and they remain so even with hugely improved computing power. Such recursions are frequently derived by exploiting relations between generating functions. For example, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other (easily computed) symmetric functions (power-sum and elementary symmetric functions; Ruben, 1962, Annals of Mathematical Statistics 33, 542–570; Hillier, Kan, and Wang, 2009, Econometric Theory 25, 211–242). Typically, in a recursion of this type the kth object of interest, dk, say, is expressed in terms of all lower order dj’s. In Hillier et al. (2009) we pointed out that, in the case of top-order zonal polynomials and other invariant polynomials of multiple matrix argument, a fixed length recursion can be deduced. We refer to this as a short recursion. The present paper shows that the main results in Hillier et al. (2009) can be generalized and that short recursions can be obtained for a much larger class of objects/generating functions. As applications, we show that short recursions can be obtained for various problems involving quadratic forms in noncentral normal vectors, including moments, product moments, and expectations of ratios of powers of quadratic forms. For this class of problems, we also show that the length of the recursion can be further reduced by an application of a generalization of Horner’s method (cf. Brown, 1986, SIAM Journal on Scientific and Statistical Computing 7, 689–695), producing a super-short recursion that is significantly more efficient than even the short recursion.
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10

Ramaswami, V., and D. M. Lucantoni. "Moments Of the stationary waiting time in the Gi/Ph/1 queue." Journal of Applied Probability 25, no. 3 (September 1988): 636–41. http://dx.doi.org/10.2307/3213992.

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Recursive relations for computing the higher moments of the stationary waiting time distribution in a stable GI/PH/1 queue are derived. These provide an accurate and stable technique to compute these moments.
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11

Ramaswami, V., and D. M. Lucantoni. "Moments Of the stationary waiting time in the Gi/Ph/1 queue." Journal of Applied Probability 25, no. 03 (September 1988): 636–41. http://dx.doi.org/10.1017/s0021900200041358.

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Recursive relations for computing the higher moments of the stationary waiting time distribution in a stable GI/PH/1 queue are derived. These provide an accurate and stable technique to compute these moments.
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12

Hu, Jian-Qiang, Soracha Nananukul, and Wei-Bo Gong. "A new approach to (s, S) inventory systems." Journal of Applied Probability 30, no. 4 (December 1993): 898–912. http://dx.doi.org/10.2307/3214521.

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In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm.(s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES
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13

Hu, Jian-Qiang, Soracha Nananukul, and Wei-Bo Gong. "A new approach to (s, S) inventory systems." Journal of Applied Probability 30, no. 04 (December 1993): 898–912. http://dx.doi.org/10.1017/s002190020004465x.

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In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm. (s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES
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14

Bényi, Árpád, and Saverio M. Manago. "A Recursive Formula for Moments of a Binomial Distribution." College Mathematics Journal 36, no. 1 (January 1, 2005): 68. http://dx.doi.org/10.2307/30044825.

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15

Léveillé, Ghislain, and José Garrido. "Recursive Moments of Compound Renewal Sums with Discounted Claims." Scandinavian Actuarial Journal 2001, no. 2 (January 2001): 98–110. http://dx.doi.org/10.1080/03461230152592755.

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16

Di Gesù, V., and R. M. Palenichka. "A fast recursive algorithm to compute local axial moments." Signal Processing 81, no. 2 (February 2001): 265–73. http://dx.doi.org/10.1016/s0165-1684(00)00206-1.

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17

Trigeassou, J. C., and P. Coirault. "Recursive Identification and Fault Detection Using Partial Time Moments." IFAC Proceedings Volumes 22, no. 6 (July 1989): 63–68. http://dx.doi.org/10.1016/s1474-6670(17)54349-9.

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18

Fu, Bo, Xiu Xiang Fan, Qiong Cheng, Li Li, Bo Li, and Guo Jun Zhang. "Accurate Computation of Zernike Moments in Cartesian Coordinates." Applied Mechanics and Materials 195-196 (August 2012): 615–19. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.615.

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In this paper, a novel algorithm is proposed to accurately calculate Zernike moments in Cartesian Coordinates. We connect the corners of an image pixel with the origin to construct four triangles and then assign the intensity function value of the pixel to these triangles. The Fourier Mellin moment integration of the pixel is converted to a summation of four integrations within domains of these constructed triangles. By using the trigonometric resolution, we derive the analytic equations of the four integrations of these triangles. Then, the analytic expressions of the Fourier Mellin moments and Zernike moments are obtained. The algorithm eliminates the geometric and discretization errors theoretically. Finally, a set of efficient computational recursive relations is proposed. An experiment is designed to verify the performance of the proposed algorithm.
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19

Qin, Hua Feng, Lan Qin, and Jun Liu. "A Novel Recurrence Method for the Fast Computation of Zernike Moments." Applied Mechanics and Materials 121-126 (October 2011): 1868–72. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1868.

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A new method is proposed for fast computation of Zernike moments. This method presents a recursive relation to compute the entire set of Zernike moments. The fast computation is achieved because it involves less addition and multiplication operations. The experimental results show that the proposed method for the fast computation of Zernike moments is much more efficient than existing fast methods in most cases
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20

Feng, Qunqiang, and Zhishui Hu. "On the Zagreb Index of Random Recursive Trees." Journal of Applied Probability 48, no. 04 (December 2011): 1189–96. http://dx.doi.org/10.1017/s0021900200008706.

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We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments ofZn, the Zagreb index of a random recursive tree of sizen, are obtained. We also show that the random process {Zn− E[Zn],n≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.
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21

Naishadham, K., and P. Misra. "Order recursive method of moments (ORMoM) for iterative design applications." IEEE Transactions on Microwave Theory and Techniques 44, no. 12 (1996): 2595–604. http://dx.doi.org/10.1109/22.554609.

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22

Koehl, P. "Fast Recursive Computation of 3D Geometric Moments from Surface Meshes." IEEE Transactions on Pattern Analysis and Machine Intelligence 34, no. 11 (November 2012): 2158–63. http://dx.doi.org/10.1109/tpami.2012.23.

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23

Monroy, I. T., and G. Hooghiemstra. "On a recursive formula for the moments of phase noise." IEEE Transactions on Communications 48, no. 6 (June 2000): 917–20. http://dx.doi.org/10.1109/26.848548.

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24

Walia, Ekta, and Anu Suneja. "Fast and High Capacity Digital Image Watermarking Technique Based on Phase of Zernike Moments." International Journal of Computer Vision and Image Processing 2, no. 1 (January 2012): 60–74. http://dx.doi.org/10.4018/ijcvip.2012010104.

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Zernike Moments (ZMs) are used in many image processing applications, due to their resistance against various signal processing and geometric attacks. Digital image watermarking is one of those application areas, where ZMs are widely used to insert and extract the watermark bits for digital media authentication. In all the existing ZM based watermarking techniques, magnitude of moments is used to insert and extract the watermark. In this paper, the authors’ have proposed a semi blind watermarking technique in which phase of ZMs is used for watermark insertion and extraction. Due to the use of phase of ZMs, 100% detection ratio is achieved against any geometric and other signal processing attacks. To make the proposed technique fast, q-recursive method is used to compute the Zernike polynomials. The use of q-recursive method has also increased the transparency of watermark due to its better reconstruction ability as compared to traditional moment computation method. Through detailed experimentation, it has been confirmed that the proposed watermarking technique is fast, has more imperceptibility, less Bit Error Rate (BER) and more capacity as compared to traditional ZMs magnitude based watermarking technique.
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Feng, Qunqiang, and Zhishui Hu. "On the Zagreb Index of Random Recursive Trees." Journal of Applied Probability 48, no. 4 (December 2011): 1189–96. http://dx.doi.org/10.1239/jap/1324046027.

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We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.
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26

Mikosch, Thomas, Gennady Samorodnitsky, and Laleh Tafakori. "Fractional Moments of Solutions to Stochastic Recurrence Equations." Journal of Applied Probability 50, no. 04 (December 2013): 969–82. http://dx.doi.org/10.1017/s0021900200013747.

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In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equationXt=AtXt−1+Bt,t∈Z, where ((At,Bt))t∈Zis an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p,p∈R. Special attention is given to the case whenBthas an Erlang distribution. We provide various approximations to the moments E|X0|pand show their performance in a small numerical study.
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27

Daduna, Hans. "On network flow equations and splitting formulas for Sojourn times in queueing networks." Journal of Applied Mathematics and Stochastic Analysis 4, no. 2 (January 1, 1991): 111–16. http://dx.doi.org/10.1155/s1048953391000072.

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28

Mikosch, Thomas, Gennady Samorodnitsky, and Laleh Tafakori. "Fractional Moments of Solutions to Stochastic Recurrence Equations." Journal of Applied Probability 50, no. 4 (December 2013): 969–82. http://dx.doi.org/10.1239/jap/1389370094.

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In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt−1 + Bt, t ∈ Z, where ((At, Bt))t∈Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p, p ∈ R. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.
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29

DE MARTINO, SALVATORE, SILVIO DE SIENA, RENATO FEDELE, and STEPHAN TZENOV. "MESOSCOPIC DESCRIPTION OF DYNAMICAL SYSTEMS: HIERARCHY OF RECURSIVE EQUATIONS FOR THE MOMENTS OF THE DENSITY DISTRIBUTION WITH AN APPLICATION TO CHARGED PARTICLE BEAM DYNAMICS." International Journal of Modern Physics B 18, no. 04n05 (February 20, 2004): 655–65. http://dx.doi.org/10.1142/s0217979204024276.

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The quantumlike formalism in the form of Madelung fluid has been applied to describe the collective dynamics of a mesoscopic aggregate of particles in a potential field. The scheme has been specialized to the one-degree-of-freedom dynamics of a charged particle beam in an accelerator in the presence of high-order multipole nonlinearities. A hierarchy of recursive equations satisfied by the moments of the density distribution has been obtained. It has been shown that the recursion relations can be in principle solved if a finite number of the first several moments is known. Beam dynamics in the presence of octupole and decapole nonlinearities has been studied as an example, demonstrating the above scheme. It has been shown that an appropriate mechanism can be introduced to control stability and coherence of states when high-order nonlinearities have to be taken into account.
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30

Grigutis, Andrius, and Jonas Šiaulys. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model." Mathematics 8, no. 2 (January 21, 2020): 147. http://dx.doi.org/10.3390/math8020147.

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In this paper, we prove recursive formulas for ultimate time survival probability when three random claims X , Y , Z in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time t ∈ { 1 , 2 , … } , claim Y additionally occurs at even moments of time t ∈ { 2 , 4 , … } and claim Z additionally occurs at every moment of time, which is a multiple of three t ∈ { 3 , 6 , … } . Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form { X , X + Y , X + Z , X + Y , X , X + Y + Z , … } . Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples.
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31

Mahmoud, Hosam M. "Limiting Distributions for Path Lengths in Recursive Trees." Probability in the Engineering and Informational Sciences 5, no. 1 (January 1991): 53–59. http://dx.doi.org/10.1017/s0269964800001881.

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The depth of insertion and the internal path length of recursive trees are studied. Luc Devroye has recently shown that the depth of insertion in recursive trees is asymptotically normal. We give a direct alternative elementary proof of this fact. Furthermore, via the theory of martingales, we show that In, the internal path length of a recursive tree of order n, converges to a limiting distribution. In fact, we show that there exists a random variable I such that (In – n In n)/n→I almost surely and in quadratic mean, as n → α. The method admits, in passing, the calculation of the first two moments of In.
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32

Zhang, Guojun, Zhu Luo, Bo Fu, Bo Li, Jiaping Liao, Xiuxiang Fan, and Zheng Xi. "A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments." Pattern Recognition Letters 31, no. 7 (May 2010): 548–54. http://dx.doi.org/10.1016/j.patrec.2009.12.007.

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33

Al-Sobhi, Mashail, Saman Hanif Shahbaz, and Muhammad Qaiser Shahbaz. "RECURSIVE COMPUTATION FOR MOMENTS OF ORDER STATISTICS FOR TRANSMUTED EXPONENTIAL DISTRIBUTION." Advances and Applications in Statistics 63, no. 2 (August 20, 2020): 175–89. http://dx.doi.org/10.17654/as063020175.

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34

Chen, Liu Xin, and Gen Li. "The Distributions and Moments of the First Entrance Time for Nonhomogeneous (H,Q) Process." Applied Mechanics and Materials 459 (October 2013): 173–76. http://dx.doi.org/10.4028/www.scientific.net/amm.459.173.

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In this paper, we discuss one kind of Markov Skeleton processes, nonhomogeneous (H,Q) processes. We mainly study their distributions and moments of the first entrance time, and we obtain their recursive formula and some related properties.
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35

Chen, Liu Xin, and Tong Yu. "The Distributions and Moments of the First Entrance Time for Nonhomogeneous Semi-Markov Process." Applied Mechanics and Materials 427-429 (September 2013): 2913–16. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.2913.

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In this paper we discuss one kind of nonhomogeneous (H,Q) processes, Nonhomogeneous Semi-Markov Process. We get the distributions and moments of the first entrance time for this process. And furthermore, we obtain their recursive formula.
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36

Zhang, Zhehao, and Shuanming Li. "Beta transform and discounted aggregate claims under dependency." Annals of Actuarial Science 13, no. 2 (July 13, 2018): 241–67. http://dx.doi.org/10.1017/s1748499518000209.

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AbstractThis paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical examples are provided to illustrate our results.
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37

Lemoine, Austin J. "On sojourn time in Jackson networks of queues." Journal of Applied Probability 24, no. 2 (June 1987): 495–510. http://dx.doi.org/10.2307/3214273.

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This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.
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38

Lemoine, Austin J. "On sojourn time in Jackson networks of queues." Journal of Applied Probability 24, no. 02 (June 1987): 495–510. http://dx.doi.org/10.1017/s0021900200031132.

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This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.
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39

Brandt, Andreas, Manfred Brandt, and Hannelore Sulanke. "A representation of a discrete distribution by its binomial moments." Journal of Applied Probability 27, no. 1 (March 1990): 208–14. http://dx.doi.org/10.2307/3214608.

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Let pk, k ≧ 0, be a probability distribution having finite binomial moments Br, r ≧ 0, and the probability generating function U(z) with a radius of convergence α (≧ 1). In this note explicit and recursive formulae are derived allowing computation of the pk in terms of the Br if α > 1. Ch. Jordan's formula, which holds if α > 2, turns out to be a special case.
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40

Brandt, Andreas, Manfred Brandt, and Hannelore Sulanke. "A representation of a discrete distribution by its binomial moments." Journal of Applied Probability 27, no. 01 (March 1990): 208–14. http://dx.doi.org/10.1017/s0021900200038559.

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Let pk, k ≧ 0, be a probability distribution having finite binomial moments Br, r ≧ 0, and the probability generating function U(z) with a radius of convergence α (≧ 1). In this note explicit and recursive formulae are derived allowing computation of the pk in terms of the Br if α > 1. Ch. Jordan's formula, which holds if α > 2, turns out to be a special case.
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41

Frostig, Esther. "The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process." Journal of Applied Probability 52, no. 3 (September 2015): 665–87. http://dx.doi.org/10.1239/jap/1445543839.

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Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.
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42

Frostig, Esther. "The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process." Journal of Applied Probability 52, no. 03 (September 2015): 665–87. http://dx.doi.org/10.1017/s0021900200113361.

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Abstract:
Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.
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43

Siaw, Kok Keng, Xueyuan Wu, David Pitt, and Yan Wang. "Matrix-form Recursive Evaluation of the Aggregate Claims Distribution Revisited." Annals of Actuarial Science 5, no. 2 (April 20, 2011): 163–79. http://dx.doi.org/10.1017/s1748499511000042.

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AbstractThis paper aims to evaluate the aggregate claims distribution under the collective risk model when the number of claims follows a so-called generalised (a, b, 1) family distribution. The definition of the generalised (a, b, 1) family of distributions is given first, then a simple matrix-form recursion for the compound generalised (a, b, 1) distributions is derived to calculate the aggregate claims distribution with discrete non-negative individual claims. Continuous individual claims are discussed as well and an integral equation of the aggregate claims distribution is developed. Moreover, a recursive formula for calculating the moments of aggregate claims is also obtained in this paper. With the recursive calculation framework being established, members that belong to the generalised (a, b, 1) family are discussed. As an illustration of potential applications of the proposed generalised (a, b, 1) distribution family on modelling insurance claim numbers, two numerical examples are given. The first example illustrates the calculation of the aggregate claims distribution using a matrix-form Poisson for claim frequency with logarithmic claim sizes. The second example is based on real data and illustrates maximum likelihood estimation for a set of distributions in the generalised (a, b, 1) family.
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44

Daduna, Hans. "Cycle times in a starlike network with state-dependent routing." Journal of Applied Mathematics and Simulation 1, no. 1 (January 1, 1987): 1–12. http://dx.doi.org/10.1155/s1048953388000012.

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For a star like network (central server system) with state dependent branching we compute the cycle time distribution. The Laplace-Stieltjes transform of this distribution is of product form. This allows to define a recursive algorithm for evaluation of cycle time moments of any order.
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45

Mohd Ramli, Siti, and Jiwook Jang. "Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims." Risks 2, no. 2 (May 27, 2014): 195–210. http://dx.doi.org/10.3390/risks2020195.

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46

Skoulakis, Georgios. "A Recursive Formula for Computing Central Moments of a Multivariate Lognormal Distribution." American Statistician 62, no. 2 (May 2008): 147–50. http://dx.doi.org/10.1198/000313008x304350.

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47

Deng, An-Wen, Chia-Hung Wei, and Chih-Ying Gwo. "Stable, fast computation of high-order Zernike moments using a recursive method." Pattern Recognition 56 (August 2016): 16–25. http://dx.doi.org/10.1016/j.patcog.2016.02.014.

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48

Soldea, Octavian, Mustafa Unel, and Aytul Ercil. "Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors." Pattern Recognition Letters 31, no. 11 (August 2010): 1428–36. http://dx.doi.org/10.1016/j.patrec.2010.02.009.

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49

Badescu, Andrei, and David Landriault. "Recursive Calculation of the Dividend Moments in a Multi-threshold Risk Model." North American Actuarial Journal 12, no. 1 (January 2008): 74–88. http://dx.doi.org/10.1080/10920277.2008.10597501.

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50

Jonckheere, Edmond, and Chingwo Ma. "Recursive partial realization from the combined sequence of markov parameters and moments." Linear Algebra and its Applications 122-124 (September 1989): 565–90. http://dx.doi.org/10.1016/0024-3795(89)90667-8.

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