Comparing two population proportions using confidence interval could be misleading in many cases, such </span><span style="font-family:Verdana;">as</span><span style="font-family:Ve...Comparing two population proportions using confidence interval could be misleading in many cases, such </span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> the sample size </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> small and the test </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> based on normal approximation. In this case, the only </span><span style="font-family:Verdana;">one</span><span style="font-family:Verdana;"> option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any </span><span style="font-family:Verdana;">requirements,</span><span style="font-family:Verdana;"> and can be used to perform inferences such </span><span style="font-family:Verdana;">as:</span><span style="font-family:Verdana;"> a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim </span><span style="font-family:Verdana;">that</span><span style="font-family:Verdana;"> exact distribution has the </span><span style="font-family:Verdana;">least</span><span style="font-family:Verdana;"> confidence width among Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.展开更多
Distributed quantum computation has gained extensive attention.In this paper,we consider a search problem that includes only one target item in the unordered database.After that,we propose a distributed exact Grover’...Distributed quantum computation has gained extensive attention.In this paper,we consider a search problem that includes only one target item in the unordered database.After that,we propose a distributed exact Grover’s algorithm(DEGA),which decomposes the original search problem into■n/2■parts.Specifically,(i)our algorithm is as exact as the modified version of Grover’s algorithm by Long,which means the theoretical probability of finding the objective state is 100%;(ii)the actual depth of our circuit is 8(n mod 2)+9,which is less than the circuit depths of the original and modified Grover’s algorithms,1+8■π/4√2^(n)■and 9+8■π/4√2^(n)-1/2■,respectively.It only depends on the parity of n,and it is not deepened as n increases;(iii)we provide particular situations of the DEGA on MindQuantum(a quantum software)to demonstrate the practicality and validity of our method.Since our circuit is shallower,it will be more resistant to the depolarization channel noise.展开更多
Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the...Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.展开更多
文摘Comparing two population proportions using confidence interval could be misleading in many cases, such </span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> the sample size </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> small and the test </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> based on normal approximation. In this case, the only </span><span style="font-family:Verdana;">one</span><span style="font-family:Verdana;"> option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any </span><span style="font-family:Verdana;">requirements,</span><span style="font-family:Verdana;"> and can be used to perform inferences such </span><span style="font-family:Verdana;">as:</span><span style="font-family:Verdana;"> a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim </span><span style="font-family:Verdana;">that</span><span style="font-family:Verdana;"> exact distribution has the </span><span style="font-family:Verdana;">least</span><span style="font-family:Verdana;"> confidence width among Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.
基金supported in part by the National Natural Science Foundation of China(Nos.61572532 and 61876195)the Natural Science Foundation of Guangdong Province of China(No.2017B030311011).
文摘Distributed quantum computation has gained extensive attention.In this paper,we consider a search problem that includes only one target item in the unordered database.After that,we propose a distributed exact Grover’s algorithm(DEGA),which decomposes the original search problem into■n/2■parts.Specifically,(i)our algorithm is as exact as the modified version of Grover’s algorithm by Long,which means the theoretical probability of finding the objective state is 100%;(ii)the actual depth of our circuit is 8(n mod 2)+9,which is less than the circuit depths of the original and modified Grover’s algorithms,1+8■π/4√2^(n)■and 9+8■π/4√2^(n)-1/2■,respectively.It only depends on the parity of n,and it is not deepened as n increases;(iii)we provide particular situations of the DEGA on MindQuantum(a quantum software)to demonstrate the practicality and validity of our method.Since our circuit is shallower,it will be more resistant to the depolarization channel noise.
基金Beijing Natural Science Foundation(Grant No.Z200001)National Natural Science Foundation of China(Grant Nos.11871001,11971478 and 11971001)the Fundamental Research Funds for the Central Universities(Grant No.2019NTSS18)。
文摘Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.
