E taken from Tomizawa et al. [15].Table 5. The two tables beneath show the SC-19220 medchemexpress decayed teeth of 349 female 189-year-old patients of a dental clinic in Sapporo City, for the period 2001005; from Tomizawa et al. [15]. (a) For female with left and right decayed teeth Appropriate Left 0 to 4 five to 8 9 and above Total 0 to 4 103 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 reduce and upper decayed information Upper Reduced 0 to 4 five to 8 9 and above Total 0 to four 97 20 two 119 5 to 8 62 63 six 131 9 and above 15 75 23 113 Total 174 158 31We shall compare the degrees of deviation from DS for Table 5a,b applying the confidence region for . The estimates of , applied towards 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 ^^-0.5 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 3 shows the self-confidence regions of applied for the information in Table 5a,b. We see that the self-assurance regions of usually do not overlap in both horizontal and vertical axes with regard to numerous values of . For that reason, we can conclude that the degree of deviation from DS is greater for Table 5b than for Table 5a.0.0.0.0.PSPS0.0.4 5b0.5b0.5a5a 0.0 0.0 0.two 0.four S 0.six 0.0.0 0.0 0.two 0.4 S 0.6 0.(a) = -0.0.(b) =0.5b PS 0.0.5a0.0 0.0 0.2 0.4 S 0.six 0.(c) = 1 Figure three. Approximate 95 confidence regions for , applied for the information in Table 5a,b, where = -0.five, 0, 1.five. Concluding Remarks This study proposed a generalized Nitrocefin Antibiotic 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 usually are not independent (= 0), itSymmetry 2021, 13,9 ofis essential 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 a number of datasets applying the proposed two-dimensional index, we ought to use quite a few instead of a single specified . Therefore, we advocate to pick out the various (e.g., -0.5, 0, 1) corresponding for the famous divergence. The estimator of your proposed two-dimensional index is the unbiased estimator when the sample size is big. When the sample size is small, nonetheless, the estimator with the proposed two-dimensional index may perhaps be the biased estimator. Through 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, (two) when the sample size was above 300, it had a slight bias, and (3) when the sample size was above 1000, it had nearly no bias. We think that the proposed two-dimensional ^ ^ estimator may be comparable final results towards the estimator S , while it is actually essential to confirm by simulation study. In future investigation, the above concern might be investigated.Author Contributions: Conceptualization, S.A. and S.T.; methodology, S.A. and H.H.; application, S.A. and H.H.; validation, A.I.; formal evaluation, 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 read and agreed for the published version with the manuscript. Funding: This research re.