Truncation point estimation of truncated normal samples and its applications

Shenglan Peng; Zikang Wan; Shenglan Peng; Zikang Wan

doi:10.3934/math.20221048

AIMS Mathematics

2022, Volume 7, Issue 10: 19083-19104. doi: 10.3934/math.20221048

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Research article

Truncation point estimation of truncated normal samples and its applications

Shenglan Peng ^,,
Zikang Wan

Computer Department, Jingdezhen Ceramic University, Jingdezhen 330403, China

Received: 13 June 2022 Revised: 27 July 2022 Accepted: 23 August 2022 Published: 29 August 2022
MSC : 62F10, 62P10

The moment estimates and maximum likelihood estimates of the truncation points in the truncated normal distribution are given, as well as the interval estimates for large samples. The estimation method of truncation point is applied to the assembly of DNA sequencing data, and moment estimation, maximum likelihood estimation and interval estimation of gap length are obtained. Monte Carlo simulations show that the experimental results are very close to the theoretical estimates. When the estimation method given in this paper is applied to a real DNA sequencing dataset, ideal estimation results are also obtained.
- truncated normal distribution,
- truncation point,
- moment estimation,
- maximum likelihood estimation,
- Lander-Waterman model,
- gap length
Citation: Shenglan Peng, Zikang Wan. Truncation point estimation of truncated normal samples and its applications[J]. AIMS Mathematics, 2022, 7(10): 19083-19104. doi: 10.3934/math.20221048

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Abstract

The moment estimates and maximum likelihood estimates of the truncation points in the truncated normal distribution are given, as well as the interval estimates for large samples. The estimation method of truncation point is applied to the assembly of DNA sequencing data, and moment estimation, maximum likelihood estimation and interval estimation of gap length are obtained. Monte Carlo simulations show that the experimental results are very close to the theoretical estimates. When the estimation method given in this paper is applied to a real DNA sequencing dataset, ideal estimation results are also obtained.

References

[1]	W. C. Horrace, Moments of the truncated normal distribution, J. Prod. Anal., 43 (2015), 133–138. http://dx.doi.org/10.1007/s11123-013-0381-8 doi: 10.1007/s11123-013-0381-8
[2]	J. Pender, The truncated normal distribution: Applications to queues with impatient customers, Oper. Res. Lett., 43 (2015), 40–45. https://doi.org/10.1016/j.orl.2014.10.008 doi: 10.1016/j.orl.2014.10.008
[3]	K. Pearson, A. Lee, On the generalized probable error in multiple normal correlation, Biometrika, 6 (1908), 59–68. http://dx.doi.org/10.1093/biomet/6.1.59 doi: 10.1093/biomet/6.1.59
[4]	R. A. Fisher, Properties and applications of Hh functions, in Mathematical Tables, British Association for the Advancement of Science, 1931.
[5]	C. I. Bliss, W. L. Stevens, The calculation of the time mortality curve, Ann. Appl. Biol., 24 (1937), 815–852. http://dx.doi.org/10.1111/j.1744-7348.1937.tb05058.x doi: 10.1111/j.1744-7348.1937.tb05058.x
[6]	A. Hald, Maximum likelihood estimation of the parameters of a normal distribution which is truncated at a known point, Scand. Actuar. J., 1 (1949), 119–134. http://dx.doi.org/10.1080/03461238.1949.10419767 doi: 10.1080/03461238.1949.10419767
[7]	A. K. Gupta, Estimation of the mean and standard deviation of a normal population from a censored sample, Biometrika, 39 (1952), 260–273. http://dx.doi.org/10.2307/2334023 doi: 10.2307/2334023
[8]	M. Halperin, Maximum likelihood estimation in truncated samples, Ann. Math. Stat., 23 (1952), 226–238. http://dx.doi.org/10.2307/2236448 doi: 10.2307/2236448
[9]	A. C. Cohen, Simplified estimators for the normal distribution when samples are singly censored or truncated, Technometrics, 1 (1959), 217–237. http://dx.doi.org/10.1080/00401706.1959.10489859 doi: 10.1080/00401706.1959.10489859
[10]	A. C. Cohen, Tables for maximum likelihood estimates: Singly truncated and singly censored samples, Technometrics, 3 (1961), 535–541. http://dx.doi.org/10.1080/00401706.1961.10489973 doi: 10.1080/00401706.1961.10489973
[11]	A. C. Cohen, Truncated and censored samples theory and applications, New York: Marcel Dekker, 1991.
[12]	D. S. Robson, J. H. Whitlock, Estimation of a truncation point, Biometrika, 51 (1964), 33–39. http://dx.doi.org/10.2307/2334193 doi: 10.2307/2334193
[13]	Z. W. Birnbaum, An inequality for Mill's ratio, Ann. Math. Stat., 13 (1942), 245–246. http://dx.doi.org/10.1214/aoms/1177731611 doi: 10.1214/aoms/1177731611
[14]	M. R. Sampford, Some inequalities on Mill's ratio and related functions, Ann. Math. Stat., 24 (1953), 130–132. http://dx.doi.org/10.2307/2236360 doi: 10.2307/2236360
[15]	Z. H. Yang, Y. M. Chu, On approximating Mills ratio, J. Inequal. Appl., 273 (2015), 273. http://dx.doi.org/10.1186/s13660-015-0792-3 doi: 10.1186/s13660-015-0792-3
[16]	E. S. Lander, M. S. Waterman, Genomic mapping by fingerprinting random clones, Genomics, 2 (1988), 231–239. http://dx.doi.org/10.1016/0888-7543(88)90007-9 doi: 10.1016/0888-7543(88)90007-9
[17]	J. C. Roach, C. Boysen, K. Wang, L. Hood, Pairwise end sequencing: A unified approach to genomic mapping and sequencing, Genomics, 26 (1995), 345–353. http://dx.doi.org/10.1016/0888-7543(95)80219-C doi: 10.1016/0888-7543(95)80219-C
[18]	D. R. Zerbino, E. Birney, Algorithms for de novo short read assembly using de Bruijn graphs, Genome Res., 18 (2008), 821–829. http://dx.doi.org/10.1101/gr.074492.107 doi: 10.1101/gr.074492.107
[19]	J. Foox, S. W. Tighe, C. M. Nicolet, J. M. Zook, M. Byrska-Bishop, W. E. Clarke, et al., Performance assessment of DNA sequencing platforms in the ABRF next-generation sequencing study, Nat. Biotechnol., 39 (2021), 1129–1140. http://dx.doi.org/10.1038/s41587-021-01049-5 doi: 10.1038/s41587-021-01049-5

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