Exponential family
What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:
Rhetorical operations
According to the Princeton Encyclopedia of Poetry and Poetics, the word amplification is one of the "special" topics used in epideictic poetry or ceremonial discourse, usually for praise, but it has been used to refer to both the expansion and the diminution of an idea or an argument. The use of the word needs to be defined precisely and used with care. The Princeton Encyclopedia also states that, "limits become clear only when a text signals by some other means (semantic: change of subject; syntactic: end of stanza/poem; pragmatic; change of voice, person, or form of address) a change of direction." Amplification was considered at different times in history "a subset of both inventio and dispositio. " Aristotle mentions in The Poetics "maximizing and minimizing" as important elements in relation to amplification. This is similar to the way we commonly think of amplification; that is going from something smaller and being enlarged. In "The Rhetoric", Aristotle contrasts amplification with depreciation and admits "they both derive from an enthymeme which serves to show how a thing is great or small." 
The Princeton Encyclopedia of Poetry and Poetics also tells us that Cicero in "De Oratore" "introduced the confusion between amplification and attenuation by saying that the highest distinction of eloquence consists in amplification by means of ornament, which can be used to make one's speech not only increase the importance of a subject and raise it to a higher level, but also to diminish and disparage it ". The relationship between the words 'conciseness' and 'amplification' is heavy. Nevin Laib, author of Conciseness and Amplification explains that, "We need to encourage profuseness as well as concision, to teach not just brevity but also loquacity, the ability to extend, vary, and expatiate upon one's subject at length to shape, build, augment, or alter the force and effect of communication, and to repeat oneself inventively. In classical rhetoric, this was the art of amplification. It included elaboration, emphasis, and copiousness of style." The message and understanding of amplification seems blurry to many students. Laib says, "The stylistic values implicit in our theories, pedagogy, and culture, so overwhelmingly favor consciousness, that elaboration gets lost in the learning process". 
Silva Rhetoricae provided by Dr. Gideon Burton of Brigham Young University understands amplification as something that can be used as a basic notion of imitation: to change the content of a model while retaining its form, or to change its form while retaining the content. Varying a sentence. Double Translation. Metaphrasis. Paraphrasis. Epitome.