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Indigenous breeds of cattle are suitable for varying climatic conditions of the tropical environment by virtue of a series of species-specific traits and adaptive strategies. Such traits and adaptive strategies could be generally classed into morphological/anatomical, physiological, behavioural, neuro-endocrine, haematological, and molecular and cellular features. At the same time, over the years it is found that the population of indigenous cattle is decreasing at a faster rate all over the world. This is mainly due to the preponderance of crosses of indigenous cattle with exotic/temperate high producing cattle for improved milk production. As a result, if suitable measures are not taken for conserving indigenous breeds of cattle, the diversity will go down drastically and may at one stage become highly endangered in status. For working out conservation plans and breeding strategies, the fundamental requirements include genetic characterization by means of gene and microsatellite markers along with evaluation of genetic variability, population structure and composition. Conserving the diversity of indigenous germplasm will help to choose breeds of cattle that adapt to changing climatic environment. Such an approach could help in formulating strategies for conservation and breeding plans and further could also lay the foundation for effective utilisation of indigenous cattle under different production systems.

The log-normal distribution is widely used to model positive valued data in many areas of applied research. However, sometimes the log-normal distribution does not completely satisfy the fitting expectations in every real life situations. In this paper, we introduce, investigate, and discuss a more flexible shifted hybrid log-normal distribution for which the log-normal distribution is a special case. Also, various properties, special cases and estimation procedure of the new distribution are discussed. Moreover, the performances of maximum likelihood estimators of the parameters are examined using a brief simulation study. The flexibility and performance of the newdistribution is also illustrated through two applications by fitting two real datasets of different situations.

Single server Retrial Queueing model with system repair and breakdown under non-preemptive priority is considered in this paper. The study of the model so far is mostly explored only for steady state solutions with few exceptions to Transient solutions. Though some researchers have attempted transient solution to the model analytically, the solution thus obtained is more complicated that it cannot be solved. In this context, we have found the transient numerical solution to the model using eigenvalues and eigenvectors. Time dependent system performance measures and probability distributions are evaluated and validated with steady state solutions. [ABSTRACT FROM AUTHOR]

In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model.

Objective: The purpose of this study was to evaluate if the cognitive benefit of rivastigmine is affected by the presence of orthostatic hypotension (OH) in patients with Parkinson's disease dementia (PDD). Methods: We conducted a post hoc analysis on 1,047 patients with PDD from 2 randomized controlled trials comparing rivastigmine versus placebo at week 24 (n = 501) and rivastigmine patch versus capsule at week 76 (n = 546). A drop ≥ 20 mm Hg in systolic blood pressure (SBP) or ≥ 10 in diastolic blood pressure (DBP) upon standing classified subjects as OH positive (OH+); otherwise, OH negative (OH‐). The primary end point was the Alzheimer's Disease Assessment Scale ‐ Cognitive subscale (ADAS‐Cog) at week 24 and the Mattis Dementia Rating Scale (MDRS) at week 76, using intention‐to‐treat with retrieved dropout at week 24 and observed cases at week 76, consistent with the original analyses. Results: Overall safety was comparable between OH+ (n = 288, 27.5%) and OH‐ (n = 730, 69.7%), except for higher frequency of syncope (9.2%) in the OH+ placebo arm. The placebo‐adjusted effect of rivastigmine on ADAS‐Cog at week 24 was 5.6 ± 1.2 for OH+ and 1.9 ± 0.9 in OH‐ (p = 0.0165). Among subjects with OH, the MDRS change from baseline at week 76 was higher for rivastigmine capsules versus patch (10.6 ± 2.9 vs ‐1.5 ± 3.0, p = 0.031). The overall prevalence of OH was lower for rivastigmine than placebo at week 24 (28.3% vs 44.6%, p = 0.0476). Interpretation: The cognitive benefit from rivastigmine is larger in patients with PDD with OH, possibly mediated by a direct antihypotensive effect. ANN NEUROL 2021;89:91–98 [ABSTRACT FROM AUTHOR]

The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.

The importance of Lagrangian distributions and their applicability in real-world events have been highlighted in several studies. In light of this, we create a new zero-truncated Lagrangian distribution. It is presented as a generalization of the zero-truncated binomial distribution (ZTBD) and hence named the Lagrangian zero-truncated binomial distribution (LZTBD). The moments, probability generating function, factorial moments, as well as skewness and kurtosis measures of the LZTBD are discussed. We also show that the new model’s finite mixture is identifiable. The unknown parameters of the LZTBD are estimated using the maximum likelihood method. A broad simulation study is executed as an evaluation of the well-established performance of the maximum likelihood estimates. The likelihood ratio test is used to assess the effectiveness of the third parameter in the new model. Six COVID-19 datasets are used to demonstrate the LZTBD’s applicability, and we conclude that the LZTBD is very competitive on the fitting objective.

Summary: Background: In both acute graft‐versus‐host disease (GVHD) and lupus erythematosus (LE), the patient's own tissues are subjected to immunological assault via complex mechanisms influenced by interferon (IFN) and other cytokines. Although not typically confused clinically, these entities have overlapping histopathological findings in the skin. Aim: To assess whether GVHD can be differentiated from LE using molecular methods on skin specimens. Methods: We developed a quantitative reverse transcription PCR assay based on previously identified tissue‐based biomarkers of cutaneous GVHD, and compared gene expression in GVHD with that in LE. Results: Both entities showed robust expression of IFN‐induced genes and of genes encoding proteins involved in antigen presentation, cell signalling and tissue repair. Levels of gene expression differed significantly in GVHD compared with LE, particularly those of IFN‐induced genes such as MX1,OAS3,TAP1 and STAT3 (P < 0.01). Three logistic regression models could differentiate the two entities with a high degree of certainty (receiver operating characteristic area under the curve of 1.0). Conclusion: The study demonstrates the feasibility of distinguishing between microscopically similar inflammatory dermatoses using tissue‐based molecular techniques. [ABSTRACT FROM AUTHOR]

In this paper we develop a bivariate discrete modifiedWeibull (BDMW) distribution and derived some of its important properties such as joint survival function, marginal survival function, conditional survival function, joint probability generating function and hazard rate function. The significance of additional parameter in BDMW is tested using generalized likelihood ratio test. Also we construct a finite mixture ofBDMWand established its identifiability condition. Certain properties of the mixture model are derived. The parameters of BDMW are estimated through method of maximum likelihood.