On estimating the parameter of a truncated geometric distribution by the method of moments

Kapadia, C. H.; Thomasson, R. L.

doi:10.1007/bf02504645

Cited by 15 publications

(7 citation statements)

References 4 publications

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“…truncated geometric (TG) variable. The latter is a geometric random variable truncated below and above by γ and ν, respectively, where, as before, γ and ν are two positive integers satisfying 0 < γ ≤ ν, see, e.g., Kapadia and Thomasson [23], Sandland [36], and Thomasson and Kapadia [39]. Thus, the PMF of a TG random variable Y is of the form…”

Section: 2mentioning

confidence: 97%

A discrete truncated Pareto distribution

Kozubowski

Panorska

Forister

2015

Statistical Methodology

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Section: 2mentioning

confidence: 97%

A discrete truncated Pareto distribution

Kozubowski

Panorska

Forister

2015

Statistical Methodology

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“…E r is the sample mean, as demonstrated by [15]. In this paper, we derived the second moment further.…”

Section: ( )mentioning

confidence: 81%

Truncated Geometric Bootstrap Method for Time Series Stationary Process

Olatayo¹

2014

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This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. The method was able to determine the block sizes b and probability p attached to its random selections. The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model.

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“…wherep i is the estimated parameter of the geometric probability density function that fits the distribution of residuals in C M,i best. Parameterp i is estimated from n i,j 's by the method of moments [42] aŝ…”

Section: Map Partitioning With Btbdmentioning

confidence: 99%

Depth Sequence Coding With Hierarchical Partitioning and Spatial-Domain Quantization

Shahriyar

Murshed

Ali³

et al. 2020

IEEE Trans. Circuits Syst. Video Technol.

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Depth coding in 3D-HEVC for the multiview video plus depth (MVD) architecture (i) deforms object shapes due to block-level edge-approximation; (ii) misses an opportunity for high compressibility at near-lossless quality by failing to exploit strong homogeneity (clustering tendency) in depth syntax, motion vector components, and residuals at frame-level; and (iii) restricts interactivity and limits responsiveness of independent use of depth information for "non-viewing" applications due to texture-depth coding dependency. This paper presents a standalone depth sequence coder, which operates in the lossless to near-lossless quality range while compressing depth data superior to lossy 3D-HEVC. It preserves edges implicitly by limiting quantisation to the spatial-domain and exploits clustering tendency efficiently at frame-level with a novel binary tree based decomposition (BTBD) technique. For mono-view coding of standard MVD test sequences, on average, (i) lossless BTBD achieved ×42.2 compression-ratio and −60.0 % coding gain against the pseudo-lossless 3D-HEVC, using the lowest quantisation parameter QP = 1, and (ii) near-lossless BTBD achieved −79.4 % and 6.98 dB Bjøntegaard delta bitrate (BD-BR) and distortion (BD-PSNR), respectively, against 3D-HEVC. In viewsynthesis applications, decoded depth maps from BTBD rendered superior quality synthetic-views, compared to 3D-HEVC, with −18.9 % depth BD-BR and 0.43 dB synthetic-texture BD-PSNR on average.Index Terms-Depth map sequence coding, hierarchical partitioning, lossless/near-lossless coding, multiview extension of High Efficiency Video Coding (3D-HEVC), multiview video plus depth (MVD), spatial-domain quantisation.S. Shahriyar was with the ). M. Murshed is and M. Ali was with the Faculty

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On estimating the parameter of a truncated geometric distribution by the method of moments

Cited by 15 publications

References 4 publications

A discrete truncated Pareto distribution

A discrete truncated Pareto distribution

Truncated Geometric Bootstrap Method for Time Series Stationary Process

Depth Sequence Coding With Hierarchical Partitioning and Spatial-Domain Quantization

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