E taken from Tomizawa et al. [15].Table five. The two tables under show the decayed teeth of 349 female 189-year-old sufferers of a dental clinic in Sapporo City, for the period 2001005; from Tomizawa et al. [15]. (a) For female with left and appropriate decayed teeth Right Left 0 to 4 5 to eight 9 and above Total 0 to four 103 35 three 141 5 to eight 45 84 17 146 9 and above 1 33 42 76 Total 149 152 62(b) For female with reduced and upper decayed information Upper Lower 0 to four five to eight 9 and above Total 0 to 4 97 20 two 119 5 to 8 62 63 six 131 9 and above 15 75 23 113 Total 174 158 31We shall evaluate the degrees of deviation from DS for Table 5a,b working with the self-confidence area for . The estimates of , applied to the information in Table 5a,b, are shown in Table six.Symmetry 2021, 13,eight of^ ^ Table six. Estimated indexes S and PS and estimated covariance matrix of applied to Table 5a,b. (a) For Table 5a Index ^ S 0.024 0.040 0.055 ^ PS 0.064 0.105 0.141 ^Covariate Matrix ^^-0.five 0(b) For Table 5b0.113 0.302 0.0.043 0.127 0.0.142 0.361 0.Index ^ S 0.281 0.414 0.501 ^ PS 0.233 0.356 0. ^Covariate Matrix ^^-0.5 00.962 1.526 1.0.541 0.890 1.0.472 0.884 1.Figure three shows the confidence regions of applied to the data in Table 5a,b. We see that the confidence regions of don’t overlap in each horizontal and vertical axes with regard to a number of values of . Therefore, we can conclude that the degree of deviation from DS is higher for Table 5b than for Table 5a.0.0.0.0.PSPS0.0.four 5b0.5b0.5a5a 0.0 0.0 0.2 0.4 S 0.six 0.0.0 0.0 0.2 0.4 S 0.6 0.(a) = -0.0.(b) =0.5b PS 0.0.5a0.0 0.0 0.2 0.four S 0.6 0.(c) = 1 Figure 3. Approximate 95 confidence regions for , applied to the information in Table 5a,b, exactly where = -0.five, 0, 1.5. Concluding Remarks This study proposed a generalized two-dimensional index that concurrently measures the degree of deviation from S and PS. Because the two indexes (Sand PS ) had been usedto measure the degree of deviation from S and PS are usually not independent (= 0), itSymmetry 2021, 13,9 ofis necessary to concurrently measure the degree of deviation from S and PS when we measure the degree of deviation from DS. To compare degrees of deviation from DS in quite a few datasets making use of the proposed two-dimensional index, we really should use many instead of one particular GYY4137 Description specified . Hence, we suggest to pick out the quite a few (e.g., -0.5, 0, 1) corresponding to the popular divergence. The estimator of the proposed two-dimensional index would be the unbiased estimator when the sample size is massive. When the sample size is small, Alvelestat Autophagy nevertheless, the estimator on the proposed two-dimensional index may be the biased estimator. Via simulation study, ^ Tomizawa et al. [16] investigated the performance in the estimator . Tomizawa ^ et al. [16] showed that (1) when the sample size was significantly less than 300, the estimator S had a bias, (2) when the sample size was above 300, it had a slight bias, and (three) when the sample size was above 1000, it had almost no bias. We think that the proposed two-dimensional ^ ^ estimator might be related outcomes to the estimator S , even though it really is necessary to confirm by simulation study. In future investigation, the above concern will probably be investigated.Author Contributions: Conceptualization, S.A. and S.T.; methodology, S.A. and H.H.; software program, S.A. and H.H.; validation, A.I.; formal analysis, S.A. and H.H.; writing–original draft preparation, S.A. and H.H.; writing–review and editing, A.I. and S.T. All authors have study and agreed for the published version of your manuscript. Funding: This study re.
