Unimodality of the distribution of record statistics

Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n[greater-or-equal, slanted]1, we denote the order statistics of X1,X2,...,Xn by X1,n[less-than-or-equals, slant]X2,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n. Define L(1)=1, L(n+1)=min{j: j>L(n), Xj>Xj-1,j-1}, andX(n)=XL(n),L(n), n[greater-or-equal, slanted]1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.Record statistics

NEPHROGENIC SYSTEMIC FIBROSIS: CURRENT CONCEPTS

Nephrogenic systemic fibrosis (NSF) was first described in 2000 as a scleromyxedema-like illness in patients on chronic hemodialysis. The relationship between NSF and gadolinium contrast during magnetic resonance imaging was postulated in 2006, and subsequently, virtually all published cases of NSF have had documented prior exposure to gadolinium-containing contrast agents. NSF has been reported in patients from a variety of ethnic backgrounds from America, Europe, Asia and Australia. Skin lesions may evolve into poorly demarcated thickened plaques that range from erythematous to hyperpigmented. With time, the skin becomes markedly indurated and tethered to the underlying fascia. Extracutaneous manifestations also occur. The diagnosis of NSF is based on the presence of characteristic clinical features in the setting of chronic kidney disease, and substantiated by skin histology. Differential diagnosis is with scleroderma, scleredema, scleromyxedema, graft-versus-host disease, etc. NSF has a relentlessly progressive course. While there is no consistently successful treatment for NSF, improving renal function seems to slow or arrest the progression of this condition. Because essentially all cases of NSF have developed following exposure to a gadolinium-containing contrast agent, prevention of this devastating condition involves the careful avoidance of administering these agents to individuals at risk

Estimation for the three-parameter lognormal distribution based on progressively censored data

Some work has been done in the past on the estimation of parameters of the three-parameter lognormal distribution based on complete and censored samples. In this article, we develop inferential methods based on progressively Type-II censored samples from a three-parameter lognormal distribution. In particular, we use the EM algorithm as well as some other numerical methods to determine maximum likelihood estimates (MLEs) of parameters. The asymptotic variances and covariances of the MLEs from the EM algorithm are computed by using the missing information principle. An alternative estimator, which is a modification of the MLE, is also proposed. The methodology developed here is then illustrated with some numerical examples. Finally, we also discuss the interval estimation based on large-sample theory and examine the actual coverage probabilities of these confidence intervals in case of small samples by means of a Monte Carlo simulation study.

Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications

Cumulants, cumulative distribution function, gamma mixtures, mixture distribution, moment matrix, p-point mixture, tail probability, weighted sums of chi-squares,

Invasive pulmonary aspergillosis – case report and review of literature

Invasive pulmonary aspergillosis (IPA) is a severe fungal infection with a high mortality rate. The incidence of IPA is on the rise due to an increase in the number of patients undergoing transplants and receiving chemotherapy and immunosuppressive therapy. Diagnosis is challenging due to the non-specific nature of symptoms. Voriconazole is the mainstay of therapy. We present a case of an elderly woman presenting with acute bronchitis and asthma exacerbation, who succumbed to overwhelming IPA. It is uncommon for IPA to develop in patients on short-term steroid therapy for asthma exacerbation. The possibility of aspergillosis in immunocompetent patients should be considered in those on systemic steroids and deteriorating pulmonary functions

Intracranial metastasis from prostate adenocarcinoma: a case report and literature review

Intracranial metastasis from prostate adenocarcinoma is rare. A 70-year-old African American male with a history of prostate adenocarcinoma for the last 14 years, presented to our hospital complaining of generalized weakness for the past 2 weeks. He was found to have fever with left ptosis and mild eyelid edema. Brain MRI showed dural metastasis. Two months after the first presentation, he was readmitted with a suspected acute cerebral vascular accident (CVA). CT brain showed vasogenic edema in the right subcortical, likely from intracranial metastasis. His acute neurological symptoms improved with intravenous dexamethasone. This case highlights the possibility of intracranial metastasis from prostate adenocarcinoma. With the advent of novel therapies for prostate cancer, which prolong life expectancy, intracranial metastasis from prostate adenocarcinoma may become an increasingly frequent clinical scenario