The gamma function is a central function that arises in many contexts. A wide class of inequaliti... more The gamma function is a central function that arises in many contexts. A wide class of inequalities is obtained by showing that certain gamma functions are Schur-convex coupled with majorization of two vectors.
The most important one parameter family of life distributions is the family of exponential distri... more The most important one parameter family of life distributions is the family of exponential distributions. This importance is partly due to the fact that several of the most commonly used families of life distributions are two- or three-parameter extensions of the exponential distributions. But the exponential distributions, with their constant hazard rates, form a baseline for evaluating other families. Because they have only one parameter, they are quite simple to describe and are exceptionally amenable to statistical analyses. A path-breaking paper of Epstein and Sobel (1953) brought new attention to the uses of the exponential distribution.
In this chapter, several distributions are discussed which, although wellknown, are not often enc... more In this chapter, several distributions are discussed which, although wellknown, are not often encountered as life distributions. These distributions may have survival functions that arise as products of those from earlier chapters, or they can be obtained by introducing a new parameter in a better-known distribution.
Distributions that have support contained in a known finite interval can be translated using scal... more Distributions that have support contained in a known finite interval can be translated using scale and location parameters so that the support of the distribution is contained in the interval [0, 1], but in no closed subinterval of [0, 1].
Human growth hormone (GH) is widely used as an antiaging therapy, although its use for this purpo... more Human growth hormone (GH) is widely used as an antiaging therapy, although its use for this purpose has not been approved by the U.S. Food and Drug Administration and its distribution as an antiaging agent is illegal in the United States. To evaluate the safety and efficacy of GH therapy in the healthy elderly. The authors searched MEDLINE and EMBASE databases for English-language studies published through 21 November 2005 by using such terms as growth hormone and aging. The authors included randomized, controlled trials that compared GH therapy with no GH therapy or GH and lifestyle interventions (exercise with or without diet) with lifestyle interventions alone. Included trials provided GH for 2 weeks or more to community-dwelling participants with a mean age of 50 years or more and a body mass index of 35 kg/m2 or less. The authors excluded studies that evaluated GH as treatment for a specific illness. Two authors independently reviewed articles and abstracted data. 31 articles describing 18 unique study populations met the inclusion criteria. A total of 220 participants who received GH (107 person-years) completed their respective studies. Study participants were elderly (mean age, 69 years [SD, 6]) and overweight (mean body mass index, 28 kg/m2 [SD, 2]). Initial daily GH dose (mean, 14 microg per kg of body weight [SD, 7]) and treatment duration (mean, 27 weeks [SD, 16]) varied. In participants treated with GH compared with those not treated with GH, overall fat mass decreased (change in fat mass, -2.1 kg [95% CI, -2.8 to -1.35] and overall lean body mass increased (change in lean body mass, 2.1 kg [CI, 1.3 to 2.9]) (P < 0.001), and their weight did not change significantly (change in weight, 0.1 kg [CI, -0.7 to 0.8]; P = 0.87). Total cholesterol levels decreased (change in cholesterol, -0.29 mmol/L [-11.21 mg/dL]; P = 0.006), although not significantly after adjustment for body composition changes. Other outcomes, including bone density and other serum lipid levels, did not change. Persons treated with GH were significantly more likely to experience soft tissue edema, arthralgias, carpal tunnel syndrome, and gynecomastia and were somewhat more likely to experience the onset of diabetes mellitus and impaired fasting glucose. Some important outcomes were infrequently or heterogeneously measured and could not be synthesized. Most included studies had small sample sizes. The literature published on randomized, controlled trials evaluating GH therapy in the healthy elderly is limited but suggests that it is associated with small changes in body composition and increased rates of adverse events. On the basis of this evidence, GH cannot be recommended as an antiaging therapy.
Resumen Este trabajo corresponde a la traducción al español de la Colaboración Especial publicada... more Resumen Este trabajo corresponde a la traducción al español de la Colaboración Especial publicada en The Journal of the American Medical Association en agosto de 1996, junto con el editorial How to report Randomized Controlled Trials. The Consort Statement, ...
Majorization has been used in two areas in numerical analysis: (i) finding a matrix closest to a ... more Majorization has been used in two areas in numerical analysis: (i) finding a matrix closest to a given matrix, and (ii) obtaining bounds for the condition number and norm of a matrix. Both (i) and (ii) depend on a relation between unitarily invariant norms and symmetric gauge functions (see 3.I.1) obtained by von Neumann (1937). Majorization arises from the fact that symmetric gauge functions are Schur-convex.
It is often convenient to represent a matrix in terms of other matrices that have special propert... more It is often convenient to represent a matrix in terms of other matrices that have special properties. Of the many such known representa- tions, a few are listed here that relate to the development of this book. General references for some of the material are Bellman (1960), Householder (1964), and Mirsky (1955a). An exposition of exponential and polar representations of matrices is given by de Bruijn and Szekeres (1955). For a compendium on matrix factorizations, see Bernstein (2005, Chapter 5).
Ordinarily, parameters of a distribution are thought of as being real or possibly vector-valued. ... more Ordinarily, parameters of a distribution are thought of as being real or possibly vector-valued. In this chapter, families of distributions are discussed, which are distinguished by having a parameter that is itself a distribution function. These families also have a real-valued parameter and consequently are said to be semiparametric.
The lognormal distribution, introduced in Chapter 1, can be obtainedfrom the normal distribution ... more The lognormal distribution, introduced in Chapter 1, can be obtainedfrom the normal distribution by means of a transformation. Specifically,ifY = logX has a normal distribution, thenX = e Y has a lognormaldistribution.
The gamma function is a central function that arises in many contexts. A wide class of inequaliti... more The gamma function is a central function that arises in many contexts. A wide class of inequalities is obtained by showing that certain gamma functions are Schur-convex coupled with majorization of two vectors.
The most important one parameter family of life distributions is the family of exponential distri... more The most important one parameter family of life distributions is the family of exponential distributions. This importance is partly due to the fact that several of the most commonly used families of life distributions are two- or three-parameter extensions of the exponential distributions. But the exponential distributions, with their constant hazard rates, form a baseline for evaluating other families. Because they have only one parameter, they are quite simple to describe and are exceptionally amenable to statistical analyses. A path-breaking paper of Epstein and Sobel (1953) brought new attention to the uses of the exponential distribution.
In this chapter, several distributions are discussed which, although wellknown, are not often enc... more In this chapter, several distributions are discussed which, although wellknown, are not often encountered as life distributions. These distributions may have survival functions that arise as products of those from earlier chapters, or they can be obtained by introducing a new parameter in a better-known distribution.
Distributions that have support contained in a known finite interval can be translated using scal... more Distributions that have support contained in a known finite interval can be translated using scale and location parameters so that the support of the distribution is contained in the interval [0, 1], but in no closed subinterval of [0, 1].
Human growth hormone (GH) is widely used as an antiaging therapy, although its use for this purpo... more Human growth hormone (GH) is widely used as an antiaging therapy, although its use for this purpose has not been approved by the U.S. Food and Drug Administration and its distribution as an antiaging agent is illegal in the United States. To evaluate the safety and efficacy of GH therapy in the healthy elderly. The authors searched MEDLINE and EMBASE databases for English-language studies published through 21 November 2005 by using such terms as growth hormone and aging. The authors included randomized, controlled trials that compared GH therapy with no GH therapy or GH and lifestyle interventions (exercise with or without diet) with lifestyle interventions alone. Included trials provided GH for 2 weeks or more to community-dwelling participants with a mean age of 50 years or more and a body mass index of 35 kg/m2 or less. The authors excluded studies that evaluated GH as treatment for a specific illness. Two authors independently reviewed articles and abstracted data. 31 articles describing 18 unique study populations met the inclusion criteria. A total of 220 participants who received GH (107 person-years) completed their respective studies. Study participants were elderly (mean age, 69 years [SD, 6]) and overweight (mean body mass index, 28 kg/m2 [SD, 2]). Initial daily GH dose (mean, 14 microg per kg of body weight [SD, 7]) and treatment duration (mean, 27 weeks [SD, 16]) varied. In participants treated with GH compared with those not treated with GH, overall fat mass decreased (change in fat mass, -2.1 kg [95% CI, -2.8 to -1.35] and overall lean body mass increased (change in lean body mass, 2.1 kg [CI, 1.3 to 2.9]) (P < 0.001), and their weight did not change significantly (change in weight, 0.1 kg [CI, -0.7 to 0.8]; P = 0.87). Total cholesterol levels decreased (change in cholesterol, -0.29 mmol/L [-11.21 mg/dL]; P = 0.006), although not significantly after adjustment for body composition changes. Other outcomes, including bone density and other serum lipid levels, did not change. Persons treated with GH were significantly more likely to experience soft tissue edema, arthralgias, carpal tunnel syndrome, and gynecomastia and were somewhat more likely to experience the onset of diabetes mellitus and impaired fasting glucose. Some important outcomes were infrequently or heterogeneously measured and could not be synthesized. Most included studies had small sample sizes. The literature published on randomized, controlled trials evaluating GH therapy in the healthy elderly is limited but suggests that it is associated with small changes in body composition and increased rates of adverse events. On the basis of this evidence, GH cannot be recommended as an antiaging therapy.
Resumen Este trabajo corresponde a la traducción al español de la Colaboración Especial publicada... more Resumen Este trabajo corresponde a la traducción al español de la Colaboración Especial publicada en The Journal of the American Medical Association en agosto de 1996, junto con el editorial How to report Randomized Controlled Trials. The Consort Statement, ...
Majorization has been used in two areas in numerical analysis: (i) finding a matrix closest to a ... more Majorization has been used in two areas in numerical analysis: (i) finding a matrix closest to a given matrix, and (ii) obtaining bounds for the condition number and norm of a matrix. Both (i) and (ii) depend on a relation between unitarily invariant norms and symmetric gauge functions (see 3.I.1) obtained by von Neumann (1937). Majorization arises from the fact that symmetric gauge functions are Schur-convex.
It is often convenient to represent a matrix in terms of other matrices that have special propert... more It is often convenient to represent a matrix in terms of other matrices that have special properties. Of the many such known representa- tions, a few are listed here that relate to the development of this book. General references for some of the material are Bellman (1960), Householder (1964), and Mirsky (1955a). An exposition of exponential and polar representations of matrices is given by de Bruijn and Szekeres (1955). For a compendium on matrix factorizations, see Bernstein (2005, Chapter 5).
Ordinarily, parameters of a distribution are thought of as being real or possibly vector-valued. ... more Ordinarily, parameters of a distribution are thought of as being real or possibly vector-valued. In this chapter, families of distributions are discussed, which are distinguished by having a parameter that is itself a distribution function. These families also have a real-valued parameter and consequently are said to be semiparametric.
The lognormal distribution, introduced in Chapter 1, can be obtainedfrom the normal distribution ... more The lognormal distribution, introduced in Chapter 1, can be obtainedfrom the normal distribution by means of a transformation. Specifically,ifY = logX has a normal distribution, thenX = e Y has a lognormaldistribution.
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