Three-stage estimation of the mean and variance of the normal distribution with application to an inverse coefficient of variation with computer simulation
| dc.Affiliation | October University for modern sciences and Arts (MSA) | |
| dc.contributor.author | Yousef A. | |
| dc.contributor.author | Hamdy H. | |
| dc.contributor.other | Department of Mathematics | |
| dc.contributor.other | Kuwait College of Science and Technology | |
| dc.contributor.other | Kuwait City | |
| dc.contributor.other | 27235 | |
| dc.contributor.other | Kuwait; Faculty of Management Sciences | |
| dc.contributor.other | October University for Modern Sciences and Arts | |
| dc.contributor.other | 6th October City | |
| dc.contributor.other | 12566 | |
| dc.contributor.other | Egypt | |
| dc.date.accessioned | 2020-01-09T20:40:33Z | |
| dc.date.available | 2020-01-09T20:40:33Z | |
| dc.date.issued | 2019 | |
| dc.description | Scopus | |
| dc.description.abstract | This paper considers sequentially two main problems. First, we estimate both the mean and the variance of the normal distribution under a unified one decision framework using Hall's three-stage procedure. We consider a minimum risk point estimation problem for the variance considering a squared-error loss function with linear sampling cost. Then we construct a confidence interval for the mean with a preassigned width and coverage probability. Second, as an application, we develop Fortran codes that tackle both the point estimation and confidence interval problems for the inverse coefficient of variation using a Monte Carlo simulation. The simulation results show negative regret in the estimation of the inverse coefficient of variation, which indicates that the three-stage procedure provides better estimation than the optimal. � 2019 by the authors. | en_US |
| dc.identifier.doi | https://doi.org/10.3390/math7090831 | |
| dc.identifier.doi | PubMed ID : | |
| dc.identifier.issn | 22277390 | |
| dc.identifier.other | https://doi.org/10.3390/math7090831 | |
| dc.identifier.other | PubMed ID : | |
| dc.identifier.uri | https://t.ly/GrpN9 | |
| dc.language.iso | English | en_US |
| dc.publisher | MDPI AG | en_US |
| dc.relation.ispartofseries | Mathematics | |
| dc.relation.ispartofseries | 7 | |
| dc.subject | October University for Modern Sciences and Arts | |
| dc.subject | جامعة أكتوبر للعلوم الحديثة والآداب | |
| dc.subject | University of Modern Sciences and Arts | |
| dc.subject | MSA University | |
| dc.subject | Asymptotic regret | en_US |
| dc.subject | Loss function | en_US |
| dc.subject | Normal distribution | en_US |
| dc.subject | Three-stage sampling procedure | en_US |
| dc.title | Three-stage estimation of the mean and variance of the normal distribution with application to an inverse coefficient of variation with computer simulation | en_US |
| dc.type | Article | en_US |
| dcterms.isReferencedBy | Mukhopadhyay, N., de Silva, B., (2009) Sequential Methods and Their Applications, , CRC: New York, NY, USA; Degroot, M.H., (1970) Optimal Statistical Decisions, , McGraw-Hill: New York, NY, USA; Dantzig, G.B., On the nonexistence of tests of 'students' hypothesis having power functions independent of s (1940) Ann. Math. Stat, 11, pp. 186-192; Hall, P., Asymptotic theory and triple sampling of sequential estimation of a mean (1981) Ann. Stat, 9, pp. 1229-1238; Anscombe, F.J., Sequential estimation (1953) J. Roy. Stat. Soc, 15, pp. 1-21; Robbins, H., (1959) Sequential Estimation of the Mean of a Normal Population. Probability and Statistics (Harald Cramer Volume), pp. 235-245. , Almquist and Wiksell: Uppsala, Sweden; Chow, Y.S., Robbins, H., On the asymptotic theory of fixed width sequential confidence intervals for the mean (1965) Ann. Math. Stat, 36, pp. 1203-1212; Stein, C., A two-sample test for a linear hypothesis whose power is independent of the variance (1945) Ann. Math. Stat, 16, pp. 243-258; Cox, D.R., Estimation by double sampling (1952) Biometrika, 39, pp. 217-227; Mukhopadhyay, N., Sequential estimation of a location parameter in exponential distributions (1974) Calcutta Stat. Assoc. Bull, 23, pp. 85-95; Mukhopadhyay, N., Hilton, G.F., Two-stage and sequential procedures for estimating the location parameter of a negative exponential distribution (1986) S. Afr. Stat. J, 20, pp. 117-136; Mukhopadhyay, N., Darmanto, S., Sequential estimation of the difference of means of two negative exponential populations (1988) Seq. Anal, 7, pp. 165-190; Mukhopadhyay, N., Hamdy, H.I., On estimating the difference of location parameters of two negative exponential distributions (1984) Can. J. Stat, 12, pp. 67-76; Ghosh, M., Mukhopadhyay, N., Sequential point estimation of the parameter of a rectangular distribution (1975) Calcutta Stat. Assoc. Bull, 24, pp. 117-122; Mukhopadhyay, N., Ekwo, M.E., Sequential estimation problems for the scale parameter of a Pareto distribution (1987) Scand. Actuar. J, pp. 83-103; Sinha, B.K., Mukhopadhyay, N., Sequential estimation of a bivariate normal mean vector (1976) Sankhya Ser. B, 38, pp. 219-230; Zacks, S., Sequential estimation of the mean of a lognormal distribution having a prescribed proportional closeness (1966) Ann. Math. Stat, 37, pp. 1688-1696; Khan, R.A., Sequential estimation of the mean vector of a multivariate normal distribution (1968) Indian Stat. Inst, 30, pp. 331-334; Ghosh, M., Mukhopadhyay, N., Sen, P.K., (1997) Sequential Estimation, , Wiley: New York, NY, USA; Hall, P., Sequential estimation saving sampling operations (1983) J. Roy. Stat. Soc. B, 45, pp. 1229-1238; Mukhopadhyay, N., A note on three-stage and sequential point estimation procedures for a normal mean (1985) Seq. Anal, 4, pp. 311-319; Mukhopadhyay, N., Sequential estimation problems for negative exponential populations (1988) Commun. Stat. Theory Methods A, 17, pp. 2471-2506; Mukhopadhyay, N., Some properties of a three-stage procedure with applications in sequential analysis (1990) Indian J. Stat Ser. A, 52, pp. 218-231; Mukhopadhyay, N., Hamdy, H.I., Al Mahmeed, M., Costanza, M.C., Three-stage point estimation procedures for a normal mean (1987) Seq. Anal, 6, pp. 21-36; Mukhopadhyay, N., Mauromoustakos, A., Three-stage estimation procedures of the negative exponential distribution (1987) Metrika, 34, pp. 83-93; Hamdy, H.I., Pallotta, W.J., Triple sampling procedure for estimating the scale parameter of Pareto distribution (1987) Commun. Stat. Theory Methods, 16, pp. 2155-2164; Hamdy, H.I., Mukhopadhyay, N., Costanza, M.C., Son, M.S., Triple stage point estimation for the exponential location parameter (1988) Ann. Inst. Stat. Math, 40, pp. 785-797; Hamdy, H.I., Remarks on the asymptotic theory of triple stage estimation of the normal mean (1988) Scand. J. Stat, 15, pp. 303-310; Hamdy, H.I., AlMahmeed, M., Nigm, A., Son, M.S., Three-stage estimation for the exponential location parameters (1989) Metron, 47, pp. 279-294; Lohr, S.L., Accurate multivariate estimation using triple sampling (1990) Ann. Stat, 18, pp. 1615-1633; Mukhopadhyay, N., Padmanabhan, A.R., A note on three-stage confidence intervals for the difference of locations: The exponential case (1993) Metrika, 40, pp. 121-128; Takada, Y., Three-stage estimation procedure of the multivariate normal mean (1993) Indian J. Stat. Ser. B, 55, pp. 124-129; Hamdy, H.I., Costanza, M.C., Ashikaga, T., On the Behrens-Fisher problem: An integrated triple sampling approach (1995), (Unpublished Manuscript); Hamdy, H.I., Performance of fixed width confidence intervals under Type II errors: The exponential case (1997) South. African Stat. J, 31, pp. 259-269; AlMahmeed, M., Hamdy, H.I., Sequential estimation of linear models in three stages (1990) Metrika, 37, pp. 19-36; AlMahmeed, M., AlHessainan, A., Son, M.S., Hamdy, H.I., Three-stage estimation for the mean of a one-parameter exponential family (1998) Korean Commun. Stat, 5, pp. 539-557; Costanza, M.C., Hamdy, H.I., Haugh, L.D., Son, M.S., Type II error performance of triple sampling fixed precision confidence intervals for the normal mean (1995) Metron, 53, pp. 69-82; Yousef, A., Kimber, A., Hamdy, H.I., Sensitivity of Normal-Based Triple Sampling Sequential Point Estimation to the Normality Assumption (2013) J. Stat. Plan. Inference, 143, pp. 1606-1618; Yousef, A., (2014) Construction a Three-Stage Asymptotic Coverage Probability for the Mean Using Edgeworth Second-Order Approximation. Selected Papers on the International Conference on Mathematical Sciences and Statistics 2013, pp. 53-67. , Springer: Singapore; Hamdy, H.I., Son, S.M., Yousef, S.A., Sensitivity Analysis of Multi-Stage Sampling to Departure of an underlying Distribution from Normality with Computer Simulations (2015) J. Seq. Anal, 34, pp. 532-558; Yousef, A., A Note on a Three-Stage Sequential Confidence Interval for the Mean When the Underlying Distribution Departs away from Normality (2018) Int. J. Appl. Math. Stat, 57, pp. 57-69; Liu, W., A k-stage sequential sampling procedure for estimation of a normal mean (1995) J. Stat. Plan. Inf, 65, pp. 109-127; Son, M.S., Haugh, H.I., Hamdy, H.I., Costanza, M.C., Controlling type II error while constructing triple sampling fixed precision confidence intervals for the normal mean (1997) Ann. Inst. Stat. Math, 49, pp. 681-692; Wald, A., (1947) Sequential Analysis, , Wiley: New York, NY, USA; Simon, G., On the cost of not knowing the variance when making a fixed-width confidence interval for the mean (1968) Ann. Math. Stat, 39, pp. 1946-1952; Martinsek, A.T., Negative regret, optimal stopping, and the elimination of outliers (1988) J. Amer. Stat. Assoc, 83, pp. 160-163; McGibney, G., Smith, M.R., An unbiased signal to noise ratio measure for magnetic resonance images (1993) Med. Phys, 20, pp. 1077-1079; Mukhopadhyay, N., Datta, S., Chattopadhyay, S., Applied Sequential Methodologies: Real-World Examples with Data Analysis (2004), CRC Press | |
| dcterms.source | Scopus |