The incubation period and generation time are key characteristics in the analysis of infectious diseases. The commonly used contact‐tracing based estimation of incubation distribution is highly influenced by the individuals' judgment on the possible date of exposure, and might lead to significant errors. On the other hand, interval censoring based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems. The distribution of generation time is usually approximated by observed serial intervals. However, it may result in a biased estimation of generation time, especially when the disease is infectious during incubation. In this paper, the theory from renewal process is partially adopted by considering the incubation period as the inter‐arrival time, and the duration between departure from Wuhan and onset of symptoms as the mixture of forward time and inter‐arrival time with censored intervals. In addition, a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation‐infectious diseases. A real case application to the current outbreak of COVID‐19 is implemented. We find that the incubation period has a median of 8.50 days (95% CI: 7.22, 9.15). The basic reproduction number in the early phase of COVID‐19 outbreak based on the proposed generation time estimation is estimated to be 2.96 (95% CI: 2.15, 3.86). This article is protected by copyright. All rights reserved

batteries on the market are nickel-metal hydride batteries, nickel-cadmium batteries, lead-acid batteries, lithium-ion batteries (LIBs), [1][2][3] etc. In addition to commercial lithium-ion batteries composed of graphite and LiCoO 2 , [4] batteries for emerging systems are also widely studied, such as silicon anode [5] and lithium sulfur batteries. [6] Presently, the widely-used secondary batteries in the industry are LIBs, [7][8][9][10][11][12][13] as shown in Figure 1.The electrolyte is an important part of the lithium-ion secondary battery. And it is the medium for realizing the migration of lithium ions between the positive and negative electrodes. To meet the ever-growing application requirements, the electrolytes can be divided into liquid electrolytes and solid-electrolytes, which can be inspired by each other. [14,15] Therefore, to improve the performance of the battery and develop new batteries, it is necessary to focus on the development and optimization of the electrolyte.The advantages of lithium-ion battery electrolytes are reflected in the large battery capacity and long cycle life, but there are still safety problems such as poor thermal stability. [16,17] Therefore, the secondary battery electrolyte is a subject worthy of in-depth study. It is of great practical significance to improve the performance of lithium-ion electrolytes by adding additives, changing solvents, lithium salts, etc. The main indicators for evaluating the performance of LIBs are safety, energy density, cycle life, and production cost, which are influenced by the properties of the electrolytes.

We study a two-sample homogeneity testing problem, in which one sample comes from a population with density f x and the other is from a mixture population with mixture density 1−λ f x λg x . This problem arises naturally from many statistical applications such as test for partial differential gene expression in microarray study or genetic studies for gene mutation. Under the semiparametric assumption g x f x e α βx , a penalized empirical likelihood ratio test could be constructed, but its implementation is hindered by the fact that there is neither feasible algorithm for computing the test statistic nor available research results on its theoretical properties. To circumvent these difficulties, we propose an EM test based on the penalized empirical likelihood. We prove that the EM test has a simple chi-square limiting distribution, and we also demonstrate its competitive testing performances by simulations. A real-data example is used to illustrate the proposed methodology.

As arsenic removal becomes a global concern, the development of removal processes for arsenic treatment is still a major challenge. With regard to environmental compatibility and cheapness, chitosan and chitosan derivatives are considered as a promising removal technology for arsenic. Chitosan and chitosan derivatives possess the properties of low cost and good sorption on the arsenic removal. The present review is concerned about the present understanding of the mechanisms involved in sorption processes. Further on, detailed discussions are given of the effects of various factors on the performance of chitosan and chitosan derivatives in arsenic treatment processes. Finally, special attention is paid to the future challenges of chitosan and chitosan derivatives utilized for industrial arsenic treatment.

The empirical best linear unbiased prediction (EBLUP) based on the nested error regression model (Battese et al. in J Am Stat Assoc 83:28-36, 1988, NER) has been widely used for small area mean estimation. Its so-called optimality largely depends on the normality of the corresponding area level and unit level error terms. To allow departure from normality, we propose a transformed NER model with an invertible transformation, and employ the maximum likelihood method to estimate the underlying parameters of the transformed NER model. Motivated by Duan's (J Am Stat Assoc 78: [605][606][607][608][609][610] 1983) smearing estimator, we propose two small area mean estimators depending on whether all the population covariates or only the population covariate means are available in addition to sample covariates. We conduct two designbased simulation studies to investigate their finite-sample performance. The simulation results indicate that compared with existing methods such as the empirical best linear unbiased prediction, the proposed estimators are nearly the same reliable when the NER model is valid and become more reliable in general when the NER model is violated. In particular, our method does benefit from incorporating auxiliary covariate information. KeywordsEmpirical best linear unbiased prediction • (Adjusted) Empirical likelihood • Nested error regression model • Small area estimation • Transformed nested error regression model B Yukun Liu