The private equity firms Carlyle Group and Hellman Friedman on Monday agreed to buy Pharmaceutical Product Development, a contract medical research company, for $3.9 billion.

Under the terms of the deal, the firms will pay $33.25 a share in cash, about 30 percent above the stock’s closing price on Friday. The buyout is expected to close in the fourth quarter.

“The sale of P.P.D. to the Carlyle Group and Hellman Friedman provides an attractive return for our shareholders, while also ensuring a secure foundation and commitment to investment, innovation and excellence for P.P.D. clients and employees as the company builds on its 25-year history of success,” Fred Eshelman, executive chairman of the company, said in a statement.

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