Almost 20,000 prescriptions for risperidone (commonly known as Risperdal), quetiapine (Seroquel) and other antipsychotic medications were written in 2014 for children 2 and younger, a 50 percent jump from 13,000 just one year before, according to the prescription data company IMS Health. Prescriptions for the antidepressant fluoxetine (Prozac) rose 23 percent in one year for that age group, to about 83,000.

The company’s data does not indicate how many children received these prescriptions (many children receive several prescriptions a year), but previous studies suggest that the number is at least 10,000. IMS Health researched the data at the request of The New York Times.

The data did not indicate the condition for which these prescriptions were written. Doctors are generally free to prescribe any medication for any purpose they see fit, so some drugs can occasionally be used in unproven and debatable ways. But the volume and rapid rise in psychotropics such as antipsychotics and antidepressants in children 2 and younger suggest a trend.

In interviews, a dozen experts in child psychiatry and neurology said that they had never heard of a child younger than 3 receiving such medication, and struggled to explain it. They presumed that parents and doctors, probably desperate and well meaning, were trying to alleviate thrashing temper tantrums — the kind that get children kicked out of day care — or an overly depressed disposition, like being strikingly inhibited, nonverbal or lethargic.

“People are doing their very best with the tools available to them,” said Dr. Mary Margaret Gleason, a pediatrician and child psychiatrist at Tulane University School of Medicine. “There’s a sense of desperation with families of children who are suffering, and the tool that most providers have is the prescription pad.”